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BEGIN:VEVENT
SUMMARY:Bhargav Bhatt (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200618T160000Z
DTEND;VALUE=DATE-TIME:20200618T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/1
DESCRIPTION:Title:
A p-adic Riemann-Hilbert functor and applications\nby Bhargav Bhatt (U
niversity of Michigan) as part of Recent Advances in Modern p-Adic Geometr
y (RAMpAGe)\n\n\nAbstract\nI will discuss an ongoing project (joint with J
acob Lurie) aiming to construct a p-adic Riemann-Hilbert functor\, attachi
ng coherent objects to constructible sheaves (with coefficients in F_p\, Z
_p or Q_p) on a compact algebraic variety over a p-adic field. I'll focus
on the case of F_p-coefficients\, which leads to a solution of some old qu
estions in commutative algebra.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART;VALUE=DATE-TIME:20200625T160000Z
DTEND;VALUE=DATE-TIME:20200625T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/2
DESCRIPTION:Title:
A p-adic transcendence criterion for CM Galois representations\nby Sea
n Howe (University of Utah) as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\n\nAbstract\nWe show that a crystalline Galois represen
tation with rational de Rham lattice admits a slope filtration with abelia
n isoclinic subquotients. As a corollary\, we find that a $p$-divisible gr
oup over $\\mathcal{O}_{\\mathbb{C_p}}$ has complex multiplication if and
only if it can be defined over a complete discretely valued subfield and i
ts Hodge-Tate filtration is algebraic -- this is a $p$-adic analog of clas
sical transcendence results for complex abelian varieties due to Schneider
\, Cohen\, and Shiga-Wolfart. More generally\, we characterize the special
points of the diamond moduli of mixed-characteristic local shtuka with on
e paw as those with algebraic Hodge-Tate and de Rham periods. The correspo
nding archimedean transcendence results for Shimura varieties fit into a b
roader framework of bialgebraicity that plays an important role in the And
re-Oort conjecture\, and\, time permitting\, we discuss some ideas of what
this might look like in the $p$-adic setting.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Scholze (University of Bonn / MPIM)
DTSTART;VALUE=DATE-TIME:20200716T160000Z
DTEND;VALUE=DATE-TIME:20200716T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/3
DESCRIPTION:Title:
Prismatic crystals and crystalline Galois representations\nby Peter Sc
holze (University of Bonn / MPIM) as part of Recent Advances in Modern p-A
dic Geometry (RAMpAGe)\n\n\nAbstract\nLet $K$ be a complete discrete valua
tion field of mixed\ncharacteristic with perfect residue field. We prove t
hat F-crystals on\nthe prismatic site of $\\mathcal{O}_K$ are equivalent t
o lattices in crystalline\n$G_K$-representations. (joint with Bhargav Bhat
t)\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wiesława Nizioł (Sorbonne / IMJ)
DTSTART;VALUE=DATE-TIME:20200730T160000Z
DTEND;VALUE=DATE-TIME:20200730T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/4
DESCRIPTION:Title:
p-adic étale cohomology of period domains\nby Wiesława Nizioł (Sorb
onne / IMJ) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)
\n\n\nAbstract\nI will show how to compute $p$-adic étale cohomology with
compact support of period domains over local fields in the case of a basi
c isocrystal for quasi-split reductive groups. This follow the method used
by Orlik in his computations of the $\\ell$-adic étale cohomology using
as a key new input the computation of Ext groups between mod-$p$ generaliz
ed Steinberg representations of $p$-adic groups. This is a joint work with
Colmez\, Dospinescu\, and Hauseux.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200702T160000Z
DTEND;VALUE=DATE-TIME:20200702T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/5
DESCRIPTION:Title:
Some examples and results on integral p-adic Hodge filtrations\nby Shi
zhang Li (University of Michigan) as part of Recent Advances in Modern p-A
dic Geometry (RAMpAGe)\n\n\nAbstract\nGiven a smooth proper scheme over a
mixed characteristic DVR\, we try to understand to what extent the special
fiber knows the Hodge numbers of the generic fiber. I'll provide some exa
mples as well as a theorem showing that in "good" situations some numbers
defined purely using the special fiber actually give the Hodge numbers of
the generic fiber. This naturally leads to consideration of Breuil-Kisin p
rismatic cohomology\, and I'll describe an example which illustrates certa
in pathological behavior of Hodge-Tate and Hodge-de Rham spectral sequence
s in mixed characteristic situations.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Zavyalov (Stanford)
DTSTART;VALUE=DATE-TIME:20200723T170000Z
DTEND;VALUE=DATE-TIME:20200723T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/6
DESCRIPTION:Title:
Mod-p Poincaré duality in p-adic geometry\nby Bogdan Zavyalov (Stanfo
rd) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAb
stract\nÉtale cohomology of $\\mathbf{F}_p$-local systems does not behav
e nicely on general smooth p-adic rigid-analytic spaces\; e.g.\, the $\\ma
thbf{F}_p$-cohomology of the 1-dimensional closed unit ball is infinite. H
owever\, it turns out that things are much better for proper p-adic rigid-
analytic spaces. For example\, Scholze used perfectoid spaces to show that
proper p-adic rigid-analytic spaces have finite cohomology for any $\\mat
hbf{F}_p$-local system. Based on Gabber's idea\, I will introduce the conc
ept of almost coherent sheaves and use it to “localize” (in an appropr
iate sense) some problems in the étale cohomology of rigid-analytic space
s. For example\, this theory (together with perfectoid spaces) can be used
to give a "new" proof of the finiteness theorem and a proof of Poincaré
duality for p-torsion coefficients on smooth and proper p-adic rigid-analy
tic spaces.\n\nThis is work in progress.\n\nPlease note that this talk beg
ins one hour later than the usual time.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial)
DTSTART;VALUE=DATE-TIME:20200806T160000Z
DTEND;VALUE=DATE-TIME:20200806T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/7
DESCRIPTION:Title:
A comparison theorem for ordinary p-adic modular forms\nby Ana Caraian
i (Imperial) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe
)\n\n\nAbstract\nI will discuss joint work in progress with Elena Mantovan
and James Newton\, whose goal is to compare ordinary completed cohomology
with (higher) Hida theory\, in the special case of the modular curve. Bot
h these notions go back to Hida\, though the former can be reinterpreted u
sing Emerton’s functor of ordinary parts applied to completed cohomology
\, and the latter has been redeveloped and expanded recently by Boxer and
Pilloni to incorporate higher coherent cohomology. Our work gives a new pr
oof to a theorem of Ohta\, that is perhaps more amenable to generalisation
. The key ingredients are the Bruhat stratification on the Hodge-Tate peri
od domain\, and the integral comparison results pioneered by Bhatt\, Morro
w and Scholze.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART;VALUE=DATE-TIME:20200709T160000Z
DTEND;VALUE=DATE-TIME:20200709T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/8
DESCRIPTION:Title:
L-packets of S-unramified regular supercuspidal representations\nby Ch
arlotte Chan (MIT) as part of Recent Advances in Modern p-Adic Geometry (R
AMpAGe)\n\n\nAbstract\nIn 2001\, Yu gave an algebraic construction of supe
rcuspidal\nrepresentations of p-adic groups (now known to be exhaustive wh
en the\nresidual characteristic is sufficiently large---Kim\, Fintzen). Th
ere\nhas since been a lot of progress towards explicitly constructing the\
nlocal Langlands correspondence: Kazhdan-Varshavsky and DeBacker-Reeder\n(
depth zero)\, Reeder and DeBacker-Spice (unramified toral)\, and\nKaletha
(regular supercuspidals). In this talk\, we present recent and\nongoing wo
rk investigating a geometric counterpart to this story. This\nis based on
joint work with Alexander Ivanov and joint work with Masao\nOi.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Magner (Boston University)
DTSTART;VALUE=DATE-TIME:20200813T160000Z
DTEND;VALUE=DATE-TIME:20200813T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/9
DESCRIPTION:Title:
On the Cohomology of Moduli of Mixed Characteristic Shtukas\nby Richar
d Magner (Boston University) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nWe review mixed characteristic shtukas an
d their moduli. These generalize the Lubin-Tate tower and other Rapoport-Z
ink spaces. Under the Kottwitz conjecture\, the cohomology of these space
s are expected to realize the local Langlands correspondence. The data de
fining these spaces involve cocharacters of a Lie group\; when the cochar
acter is minuscule\, we recover classical Rapoport-Zink spaces. In the ca
se of $\\mathrm{GL}_n$\, we show that the Kottwitz conjecture for general
cocharacters can be reduced to the minuscule case. This depends on a geom
etric Satake equivalence for the $B_{\\mathrm{dR}}$-affine Grassmanian\, d
ue to Fargues and Scholze\, and a formula of Imai on cohomology derived fr
om it.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (Harvard University)
DTSTART;VALUE=DATE-TIME:20200820T160000Z
DTEND;VALUE=DATE-TIME:20200820T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/10
DESCRIPTION:Title: Mod p Hecke algebras and perverse F_p-sheaves\nby Robert Cass (Harvar
d University) as part of Recent Advances in Modern p-Adic Geometry (RAMpAG
e)\n\n\nAbstract\nWe explain a mod $p$ version of the geometric Satake iso
morphism which gives a sheaf-theoretic description of the spherical mod $p
$ Hecke algebra. We also construct central elements in the Iwahori mod p H
ecke algebra by adapting a method due to Gaitsgory. Our proofs rely crucia
lly on the theory of $F$-singularities\, and along the way we prove new re
sults about the singularities of affine Schubert varieties. We expect thes
e results to have applications toward a mod $p$ Langlands correspondence.\
n
LOCATION:https://researchseminars.org/talk/RAMpAGe/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miaofen Chen (East China Normal University)
DTSTART;VALUE=DATE-TIME:20200910T150000Z
DTEND;VALUE=DATE-TIME:20200910T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/12
DESCRIPTION:Title: Connectedness of Kisin varieties associated to absolutely irreducible Ga
lois representations\nby Miaofen Chen (East China Normal University) a
s part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstrac
t\nAbstract: Let $K$ be a $p$-adic field. Let $\\rho$ be an $n$-dimensiona
l continuous absolutely irreducible mod $p$ representation of the absolute
Galois group of $K$. The Kisin variety is a projective scheme which param
etrizes the finite flat group schemes over the ring of integers of $K$ wit
h generic fiber $\\rho$ satisfying some determinant condition. The connect
ed components of the Kisin variety is in bijection with the connected comp
onents of the generic fiber of the flat deformation ring of $\\rho$ with g
iven Hodge-Tate weights. Kisin conjectured that the Kisin variety is conn
ected in this case. We show that Kisin's conjecture holds if $K$ is total
ly ramified with $n=3$ or the determinant condition is of a very particula
r form. We also give counterexamples to show Kisin's conjecture does not
hold in general. This is a joint work with Sian Nie.\n\nPlease note that t
his talk is one hour earlier than usual.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Gleason (Berkeley)
DTSTART;VALUE=DATE-TIME:20201001T160000Z
DTEND;VALUE=DATE-TIME:20201001T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/13
DESCRIPTION:Title: On the geometric connected components of moduli of mixed characteristic s
htukas\nby Ian Gleason (Berkeley) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nBy a theorem of Scholze and Wein
stein\, moduli spaces of mixed characteristic shtukas generalize Rapoport-
Zink spaces at infinite level. In this talk\, we describe the structure of
the set of geometric connected components of those moduli spaces that are
associated to the data $(G\,b\,\\mu)$ with $G$ an unramified reductive gr
oup and $(b\,\\mu)$ HN-irreducible. This result generalizes the work of Ch
en on the geometric connected components of unramified HN-irreducible Rapo
port-Zink spaces of EL and PEL type. In the interest of time\, we only ske
tch the part of the proof that requires a new geometric ingredient: namely
\, the specialization map for Scholze's category of diamonds.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (University of Chicago)
DTSTART;VALUE=DATE-TIME:20200827T160000Z
DTEND;VALUE=DATE-TIME:20200827T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/14
DESCRIPTION:Title: On the locally analytic vectors of the completed cohomology of modular cu
rves\nby Lue Pan (University of Chicago) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe study locally analytic
vectors of the completed cohomology of\nmodular curves and determine eige
nvectors of a rational Borel subalgebra\nof gl_2(Q_p). As applications\, w
e are able to prove a classicality result\nfor overconvergent eigenform of
weight one and give a new proof of\nFontaine-Mazur conjecture in the irre
gular case under some mild\nhypothesis. One technical tool is relative Sen
theory which allows us to\nrelate infinitesimal group action with Hodge(-
Tate) structure.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Wear (Utah)
DTSTART;VALUE=DATE-TIME:20201008T160000Z
DTEND;VALUE=DATE-TIME:20201008T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/15
DESCRIPTION:Title: Perfectoid covers of abelian varieties and the weight-monodromy conjectur
e\nby Peter Wear (Utah) as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\n\nAbstract\nDeligne's weight-monodromy conjecture give
s control over the zeros of local factors of L-functions of varieties at p
laces of bad reduction. His proof in characteristic p was a step in his pr
oof of the generalized Weil conjectures. Scholze developed the theory of p
erfectoid spaces to transfer Deligne's proof to characteristic 0\, proving
the conjecture for complete intersections in toric varieties. Building on
Scholze's techniques\, we prove the weight-monodromy conjecture for compl
ete intersections in abelian varieties. Part of this talk will discuss joi
nt work with Blakestad\, Gvirtz\, Heuer\, Shchedrina\, Shimizu\, and Yao.\
n
LOCATION:https://researchseminars.org/talk/RAMpAGe/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Viehmann (TU Munchen)
DTSTART;VALUE=DATE-TIME:20200917T160000Z
DTEND;VALUE=DATE-TIME:20200917T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/16
DESCRIPTION:Title: Newton strata in the weakly admissible locus\nby Eva Viehmann (TU Mun
chen) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\n
Abstract\nGiven a reductive group G over a p-adic local field and a minusc
ule\ncocharacter\, Rapoport and Zink constructed an open subspace inside t
he\nassociated adic flag variety\, called p-adic period domain or weakly\n
admissible locus. These are vast generalizations of Drinfeld upper half\ns
paces. Recently\, Caraiani and Scholze defined a Newton stratification\non
adic flag varieties. The unique open Newton stratum coincides with\nthe s
o-called admissible locus\, and is contained in the weakly\nadmissible loc
us. However\, in most cases the two spaces do not coincide.\nIn my talk\,
I describe which of the other Newton strata intersect the\nweakly admissib
le locus.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Clausen (Copenhagen)
DTSTART;VALUE=DATE-TIME:20200924T160000Z
DTEND;VALUE=DATE-TIME:20200924T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/17
DESCRIPTION:Title: Quasicoherent sheaves on rigid analytic spaces\nby Dustin Clausen (Co
penhagen) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n
\n\nAbstract\nI will describe a theory of "solid" quasicoherent sheaves on
rigid analytic spaces\, and explain how its basic properties give concept
ually simple proofs of various foundational results concerning vector bund
les and coherent sheaves in rigid geometry. This is joint work with Peter
Scholze.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:*No meeting*
DTSTART;VALUE=DATE-TIME:20200903T160000Z
DTEND;VALUE=DATE-TIME:20200903T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/18
DESCRIPTION:by *No meeting* as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haoyang Guo (Michigan)
DTSTART;VALUE=DATE-TIME:20201015T160000Z
DTEND;VALUE=DATE-TIME:20201015T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/19
DESCRIPTION:Title: Hodge-Tate decomposition for non-smooth rigid spaces\nby Haoyang Guo
(Michigan) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\
n\n\nAbstract\nGiven a smooth projective variety over a $p$-adic field\, i
ts $p$-adic étale cohomology admits a natural Galois equivariant decompos
ition\, called Hodge-Tate decomposition. The decomposition builds a connec
tion between the underlying $p$-adic Galois representation and the cohomol
ogy of differentials\, relating arithmetic and geometric information altog
ether. In this talk\, we generalize Hodge-Tate decomposition to non-smooth
rigid spaces\, and show how to compute $p$-adic étale cohomology via coh
omology of Deligne-Du Bois complexes.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cong Xue (Cambridge)
DTSTART;VALUE=DATE-TIME:20201105T170000Z
DTEND;VALUE=DATE-TIME:20201105T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/20
DESCRIPTION:Title: Smoothness of the cohomology sheaves of stacks of shtukas\nby Cong Xu
e (Cambridge) as part of Recent Advances in Modern p-Adic Geometry (RAMpAG
e)\n\n\nAbstract\nLet $X$ be a smooth projective geometrically connected c
urve\nover a finite field $\\mathbb{F}_q$. Let $G$ be a connected reductiv
e group over the\nfunction field of $X$. For every finite set $I$ and ever
y representation of\n$(\\check{G})^I$\, where $\\check{G}$ is the Langland
s dual group of $G$\, we have\na stack of shtukas over $X^I$. For every de
gree\, we have a compact support\nl-adic cohomology sheaf over $X^I$.\n\nI
n this talk\, I will recall some properties of these sheaves. I will\ntalk
about a work in progress which proves that these sheaves are\nind-smooth
over $X^I$.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Achinger (IMPAN Warsaw)
DTSTART;VALUE=DATE-TIME:20201022T160000Z
DTEND;VALUE=DATE-TIME:20201022T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/21
DESCRIPTION:Title: Hodge theory over $\\mathbf{C}((t))$\nby Piotr Achinger (IMPAN Warsaw
) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbst
ract\nI will describe some ways in which Hodge theory makes its way into t
he\ngeometry of rigid-analytic varieties over $\\mathbf{C}((t))$. Namely\,
such spaces\nhave a "Betti realization"\, well-defined up to homotopy (jo
int work\nwith Talpo)\, and their cohomology carries a mixed Hodge Structu
re\n(Steenbrink\, Stewart-Vologodsky\, Berkovich). The notion of "projecti
ve\nreduction" introduced by Li and studied by Hansen-Li is a good working
\nanalog of the Kaehler condition. In this case\, Hodge symmetry holds\,\n
even though it fails in some cases over the $p$-adic numbers (Petrov).\nMo
reover\, there is a Riemann-Hilbert correspondence (work in\nprogress)\, w
hich should allow us to define variations of mixed Hodge\nstructure in thi
s context. All of these analogs rely on corresponding\nstatements regardin
g the logarithmic special fiber of a semistable\nmodel. Open problems abou
nd.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Reinecke (IAS)
DTSTART;VALUE=DATE-TIME:20201119T170000Z
DTEND;VALUE=DATE-TIME:20201119T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/22
DESCRIPTION:Title: The cohomology of moduli of curves at infinite level\nby Emanuel Rein
ecke (IAS) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\
n\n\nAbstract\nBy work of Harer\, the Betti cohomology of the moduli space
of smooth\, complex curves of genus $g > 1$ vanishes in degrees above $4g
- 5$. In my talk\, I give a new perspective on this result which uses $p$
-adic geometry. The approach also yields statements about moduli of stable
curves and curves of compact type that are not covered by Harer's methods
.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Hamann (Princeton)
DTSTART;VALUE=DATE-TIME:20201029T160000Z
DTEND;VALUE=DATE-TIME:20201029T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/23
DESCRIPTION:Title: Compatibility of the Fargues-Scholze and Gan-Takeda Local Langlands Corre
spondences\nby Linus Hamann (Princeton) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nIn upcoming work\, Fargues
and Scholze construct a candidate for a general local Langlands correspon
dence\, \nassociating to a smooth irreducible representation of a connect
ed reductive group $G/\\mathbf{Q}_{p}$ a continuous semisimple Weil parame
ter\, using the action of excursion operators\non the moduli space of $G$-
bundles on the Fargues-Fontaine curve. It is a natural question to ask whe
ther this correspondence is compatible with known instances of the local L
anglands correspondence after semi-simplification. For $G = \\mathrm{GL}_{
n}$\, this compatibility is deduced from the fact that correspondence of H
arris-Taylor is realized in the cohomology of the Lubin-Tate tower at infi
nite level\, via its interpretation as a moduli space of mixed characteris
tic shtukas. For $G = \\mathrm{GSp}_{4}$ or its inner form $\\mathrm{GU}_{
2}(D)$\, there is a local Langlands correspondence constructed by Gan-Take
da and Gan-Tantono\, respectively. We will discuss upcoming work related t
o proving compatibility in this case. Similar to the case of $\\mathrm{GL}
_{n}$\, this involves realizing this local Langlands correspondence in the
cohomology of the local Shimura varieties at infinite level associated wi
th these groups. We do this by applying basic uniformization of these loca
l Shimura varieties due to Shen\, as well as results on Galois representat
ions in the cohomology of the relevant global Shimura varieties due to Sor
ensen and Kret-Shin. After proving this compatibility\, we employ various
new ideas from the geometry of the Fargues Scholze correspondence to obtai
n a complete description of the $\\rho$-isotypic part of the cohomology of
this local Shimura variety at infinite level\, where $\\rho$ is a represe
ntation of $G$ with supercuspidal Gan-Takeda or Gan-Tantono parameter\, th
ereby verifying the strongest form of the Kottwitz conjecture for these sp
ecific representations.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UCSD)
DTSTART;VALUE=DATE-TIME:20201112T170000Z
DTEND;VALUE=DATE-TIME:20201112T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/24
DESCRIPTION:Title: Several forms of Drinfeld's lemma\nby Kiran Kedlaya (UCSD) as part of
Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThe te
rm "Drinfeld's lemma" refers to several related statements about\nthe beha
vior of etale fundamental groups under formation of products in\nmixed or
positive characteristic. We discuss statements of this form in\nthe contex
ts of schemes (after Drinfeld and Lau)\, perfectoid spaces (after\nScholze
-Weinstein\, Carter-Kedlaya-Zabradi\, and Fargues-Scholze)\, and\nF-isocry
stals (work in progress).\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (King's College London)
DTSTART;VALUE=DATE-TIME:20201203T170000Z
DTEND;VALUE=DATE-TIME:20201203T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/25
DESCRIPTION:Title: Symmetric power functoriality and the geometry of eigenvarieties\nby
James Newton (King's College London) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nI will discuss work with Jack Tho
rne on symmetric power functoriality for modular forms\, with a focus on t
he role of eigenvarieties and their geometry.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT/IAS)
DTSTART;VALUE=DATE-TIME:20201210T170000Z
DTEND;VALUE=DATE-TIME:20201210T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/26
DESCRIPTION:Title: Equivariant localization\, parity sheaves\, and cyclic base change\nb
y Tony Feng (MIT/IAS) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nLaﬀorgue and Genestier-Laﬀorgue have constru
cted the global and (semisimpliﬁed) local Langlands correspondences for
arbitrary reductive groups over function ﬁelds. I will explain some rece
ntly established properties of these correspondences regarding base change
functoriality: existence of transfers for mod $p$ automorphic forms throu
gh $p$-cyclic base change in the global correspondence\, and Tate cohomolo
gy realizes $p$-cyclic base change in the mod $p$ local correspondence. In
particular\, the local statement verifies a conjecture\nof Treumann-Venka
tesh. The proofs combine Lafforgue’s theory with equivariant localizatio
n arguments for shtukas as well as recent advances in modular representati
on theory\, namely parity sheaves and Smith-Treumann theory. Compared with
previous iterations of the talk\,\nthis time the talk will emphasize the
role of the new representation-theoretic tools\, during the extra 20 minut
es.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynnelle Ye (Stanford)
DTSTART;VALUE=DATE-TIME:20201217T170000Z
DTEND;VALUE=DATE-TIME:20201217T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/27
DESCRIPTION:Title: The valuative criterion for properness for eigenvarieties\nby Lynnell
e Ye (Stanford) as part of Recent Advances in Modern p-Adic Geometry (RAMp
AGe)\n\n\nAbstract\nThe question of whether the Coleman-Mazur eigencurve s
atisfies the valuative criterion for properness was first asked by Coleman
and Mazur in 1998 and settled by Diao and Liu in 2016 using deep\, powerf
ul Galois-theoretic machinery. We will discuss a new proof which is short
and explicit and uses no Galois theory. Instead we adapt an earlier method
of Buzzard and Calegari based on elementary properties of overconvergent
modular forms\, for which we have to extend Pilloni's geometric constructi
on of overconvergent forms of arbitrary weight farther into the supersingu
lar locus. We will also discuss generalizations in progress.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Ivanov (Universitat Bonn)
DTSTART;VALUE=DATE-TIME:20210107T170000Z
DTEND;VALUE=DATE-TIME:20210107T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/28
DESCRIPTION:Title: On $p$-adic Deligne--Lusztig spaces\nby Alexander Ivanov (Universitat
Bonn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\
nAbstract\nWe discuss a new definition of $p$-adic Deligne--Lusztig spaces
\,\nas arc-sheaves on perfect algebras over the residue field. We look the
n\nat some fundamental properties of these sheaves. In particular\, we sho
w\nthat they are ind-representable in many cases. Along the way we discuss
\na general result saying that the (perfect) loop space of a\nquasi-projec
tive scheme over $\\mathbf{Q}_p$ is an arc-sheaf.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin
DTSTART;VALUE=DATE-TIME:20210114T180000Z
DTEND;VALUE=DATE-TIME:20210114T192000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/29
DESCRIPTION:Title: Galois representations over pseudorigid spaces\nby Rebecca Bellovin a
s part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstrac
t\nIn the past few years\, extended eigenvarieties with\n"boundary" in pos
itive characteristic have been constructed as\n"pseudorigid spaces". I wi
ll discuss the construction of\n$(\\varphi\,\\Gamma)$-modules for $p$-adic
Galois representations with\ncoefficients in pseudoaffinoid algebras and
discuss some of their\nproperties. I will conclude by giving applications
to the extended\neigencurve at the boundary of weight space.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART;VALUE=DATE-TIME:20210121T170000Z
DTEND;VALUE=DATE-TIME:20210121T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/30
DESCRIPTION:Title: Cohomology of the Drinfeld tower: a family affair\nby Gabriel Dospine
scu (ENS Lyon) as part of Recent Advances in Modern p-Adic Geometry (RAMpA
Ge)\n\n\nAbstract\nI will report on joint work with Pierre Colmez and Wies
lawa\nNiziol\, refining our previous results on the cohomology of the cove
rings\nof the Drinfeld half-space for GL_2(Q_p). Here we deal with integra
l and\n“family" aspects of the cohomology\, as well as the realisation o
f the\np-adic local Langlands correspondence for GL_2(Q_p) for all\ntwo-di
mensional representations of the absolute Galois group of Q_p. A\nkey role
is played by a re-interpretation of Scholze’s functor.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Heuer (Universitat Bonn)
DTSTART;VALUE=DATE-TIME:20210128T170000Z
DTEND;VALUE=DATE-TIME:20210128T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/31
DESCRIPTION:Title: v-vector bundles on rigid spaces\nby Ben Heuer (Universitat Bonn) as
part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\
nThis talk is about the difference between vector bundles on a\nsmooth rig
id space X and v-vector bundles on the associated diamond. In\nthe case of
line bundles\, I will explain how this difference can be\nfully described
in terms of differentials using a "Hodge-Tate logarithm"\nmap. For proper
X\, I will explain how one can use the proétale universal\ncover of X to
interpret this description as a p-adic Simpson\ncorrespondence of rank 1.
\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART;VALUE=DATE-TIME:20210318T150000Z
DTEND;VALUE=DATE-TIME:20210318T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/32
DESCRIPTION:Title: Partial classicality of Hilbert modular forms\nby Chi-Yun Hsu (UCLA)
as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstra
ct\nLet $p$ be an inert prime in a totally real field $F$ for simplicity.
Using the method of analytic continuation\, Kassaei proved a classicality
theorem: an overconvergent Hilbert $U_p$-eigenform is automatically classi
cal when the slope is small compared to the weights. In analogy to overcon
vergent forms\, which are defined over a strict neighborhood of the zero l
ocus of the Hasse invariant\, one can define partially classical overconve
rgent forms as defined over a strict neighborhood of the zero locus of a s
ub-collection of partial Hasse invariants. Under a weaker small slope cond
ition depending on the relevant weights\, we show that an overconvergent $
U_p$-eigenform is partially classical.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Petrov (Harvard)
DTSTART;VALUE=DATE-TIME:20210304T160000Z
DTEND;VALUE=DATE-TIME:20210304T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/33
DESCRIPTION:Title: Geometrically irreducible $p$-adic local systems are de Rham up to a twis
t\nby Alexander Petrov (Harvard) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $K$ be a p-adic field. Althou
gh there are plenty of non-de Rham representations of the Galois group of
$K$\, it turns out that for any smooth variety $X$ over $K$ and a $\\overl
ine{\\mathbf{Q}}_p$-local system $L$ on $X$ such that the restriction of $
L$ to $X_{\\overline{K}}$ is irreducible\, there exists a character of the
Galois group of $K$ such that twisting by this character turns $L$ into a
de Rham local system. In particular\, for a geometrically irreducible $\\
overline{\\mathbf{Q}}_p$-local system on a smooth variety over a number fi
eld\, the associated projective representation of the fundamental group au
tomatically satisfies the assumptions of the relative Fontaine-Mazur conje
cture.\n\nThe proof uses $p$-adic Riemann-Hilbert correspondence in the fo
rm constructed by Liu and Zhu as well as its logarithmic version construct
ed by Diao-Lan-Liu-Zhu and their decompletions developed by Shimizu.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Kramer-Miller (UC Irvine)
DTSTART;VALUE=DATE-TIME:20210211T170000Z
DTEND;VALUE=DATE-TIME:20210211T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/34
DESCRIPTION:Title: The ramification of p-adic representations coming from geometry\nby J
oe Kramer-Miller (UC Irvine) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nThe purpose of this talk is to explain a
geometric analogue of Sen's classical theorem\, which describes the close
relationship between $p$-adic Lie filtrations and ramification filtrations
for $p$-adic fields. Let $X$ be a smooth variety over a perfect field $k$
with characteristic $p>0$\, let $D\\subset X$ be a reduced divisor with s
mooth normal crossings\, and let $U=X\\backslash D$. Consider a continuous
representation $\\rho:\\pi_1(U) \\to GL(\\Z_p)$\, which gives rise to an
$p$-adic Lie tower of \\'etale covers $U_n \\to U$. We may associate to ea
ch cover a Swan divisor $sw(U_n/U)$\, supported on $D$\, using the ramific
ation filtration of Abbes-Saito. In general\, the growth of these divisors
can be arbitrarily wild. Instead\, we restrict ourselves to representatio
ns that are ordinary geometric (e.g. $\\rho$ arises as the $p$-adic Tate m
odule of a family of ordinary Abelian varieties). Our main result states t
hat for $\\rho$ ordinary geometric\, there exists integers $c_1>c_0>0$ suc
h that $c_1p^{2n} D > sw(U_n/U) > c_0 p^{2n}D$. This says that even though
$\\rho$ has infinite monodromy\, the Swan conductors $sw(U_n/U)$ grow as
`slowly as possible'.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Fox (Oregon)
DTSTART;VALUE=DATE-TIME:20210225T170000Z
DTEND;VALUE=DATE-TIME:20210225T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/35
DESCRIPTION:Title: Supersingular loci of some unitary Shimura varieties\nby Maria Fox (O
regon) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\
nAbstract\nUnitary Shimura varieties are moduli spaces of abelian varietie
s with an action of a quadratic imaginary field\, and extra structure. In
this talk\, we'll discuss specific examples of unitary Shimura varieties w
hose supersingular loci can be concretely described in terms of Deligne-Lu
sztig varieties. By Rapoport-Zink uniformization\, much of the structure o
f these supersingular loci can be understood by studying an associated mod
uli space of p-divisible groups (a Rapoport-Zink space). We'll discuss the
geometric structure of these associated Rapoport-Zink spaces as well as s
ome techniques for studying them.\n\n**Note from the organizers: Starting
on March 4\, the seminar will be moving one hour earlier\, to 11:00 Bosto
n / 17:00 Paris. This change does not apply to the talk on March 11\, whi
ch is still at 12:00 Boston / 18:00 Paris. We apologize for any inconveni
ence.**\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Judith Ludwig (Heidelberg)
DTSTART;VALUE=DATE-TIME:20210408T150000Z
DTEND;VALUE=DATE-TIME:20210408T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/36
DESCRIPTION:Title: Endoscopic points on the SL(2)-eigencurve\nby Judith Ludwig (Heidelbe
rg) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAb
stract\nAfter recalling some background on Langlands correspondences and $
L$-packets for $\\mathrm{SL}(2)$\, we will study endoscopy in the setting
of eigenvarietes. I will explain the existence of some interesting $p$-adi
c automorphic forms that can be seen using the $\\mathrm{SL}(2)$-eigencurv
e at certain endoscopic points. Finally I will report on work in progress
with C. Johansson\, where we study the $\\mathrm{SL}(2)$-eigencurve at en
doscopic points via the Coleman-Mazur eigencurve.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mann (Bonn)
DTSTART;VALUE=DATE-TIME:20210218T170000Z
DTEND;VALUE=DATE-TIME:20210218T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/37
DESCRIPTION:Title: $p$-adic six functors on diamonds\nby Lucas Mann (Bonn) as part of Re
cent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nMotivated
by $p$-adic Poincaré duality in rigid geometry\, we develop a $p$-adic s
ix functor formalism on rigid varieties\, or more generally for diamonds.
This is achieved by defining a category of "quasi-coherent $\\mathcal{O}_X
^+/p$-modules" on a diamond $X$ and then using the recent development of a
quasi-coherent 6-functor formalism on schemes by Clausen-Scholze to obtai
n a similar 6-functor formalism on diamonds. One easily deduces the desire
d p-adic Poincaré duality on a smooth proper rigid variety $X$ in mixed c
haracteristic\, noting that by Scholze's primitive comparison theorem\, $\
\mathbb F_p$-cohomology on $X$ can be computed via cohomology of the sheaf
$O_X^+/p$. Of course\, our p-adic 6-functor formalism allows for many mor
e potential applications\; for example\, we expect to gain new insights in
the $p$-adic Langlands program.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroki Kato (Paris Saclay)
DTSTART;VALUE=DATE-TIME:20210311T170000Z
DTEND;VALUE=DATE-TIME:20210311T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/38
DESCRIPTION:Title: Etale cohomology of algebraizable rigid analytic varieties via nearby cyc
les over general bases\nby Hiroki Kato (Paris Saclay) as part of Recen
t Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nOne of the m
ost fundamental results in the study of étale cohomology of rigid analyti
c varieties is the comparison with the nearby cycle cohomology\, which giv
es a canonical isomorphism between the cohomology of an algebraizable rigi
d analytic variety and the cohomology of the nearby cycle. \nI will discus
s a generalization of this comparison result to the relative case: For an
algebraizable morphism\, the compactly supported higher direct image sheav
es are identified\, up to replacing the target by a blowup\, with a genera
lization of the nearby cycle cohomology\, which is given by the theory of
nearby cycles over general bases. \nThis result can be used to show the ex
istence of a tubular neighborhood that doesn’t change the cohomology for
algebraizable families.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guido Bosco (IMJ)
DTSTART;VALUE=DATE-TIME:20210617T160000Z
DTEND;VALUE=DATE-TIME:20210617T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/40
DESCRIPTION:Title: Rational p-adic Hodge theory for non-proper rigid-analytic varieties\
nby Guido Bosco (IMJ) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nThe goal of this talk will be to discuss the rat
ional p-adic Hodge\ntheory of general smooth rigid-analytic varieties. The
study of this\nsubject for varieties that are not necessarily proper (e.g
. Stein) is\nmotivated in part by the desire of finding a geometric incarn
ation of\nthe p-adic Langlands correspondence in the cohomology of local S
himura\nvarieties. In this context\, one difficulty is that the relevant\n
cohomology groups (such as the p-adic (pro-)étale\, and de Rham ones) are
\nusually infinite-dimensional\, and\, to study them\, it becomes importan
t\nto exploit the topological structure that they carry. But\, in doing so
\,\none quickly runs into several topological issues: for example\, the de
\nRham cohomology groups of a smooth affinoid space are\, in general\, not
\nHausdorff. We will explain how to overcome these issues\, using the\ncon
densed and solid formalisms recently developed by Clausen and\nScholze\, a
nd we will report on a comparison theorem describing the\ngeometric p-adic
(pro-)étale cohomology in terms of de Rham data\, for a\nlarge class of
smooth rigid-analytic varieties defined over a p-adic\nfield. In particula
r\, we recover results of Colmez\, Dospinescu\, and\nNizioł.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (FU Berlin)
DTSTART;VALUE=DATE-TIME:20210415T150000Z
DTEND;VALUE=DATE-TIME:20210415T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/41
DESCRIPTION:Title: Connections and Symmetric Differential Forms\nby Hélène Esnault (FU
Berlin) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
n\nAbstract\n(work in progress with Michael Groechenig)\nIf $X$ is smooth
complex projective and does not have any non-trivial symmetric differentia
l forms\, then all its complex local systems have finite monodromy (Bruneb
arbe-Klingler-Totaro ’13\, in answer to a question I had posed). The pro
of relies on positivity theory stemming from Hodge Theory.\n\nThe aim is t
o understand a suitable formulation in characteristic $p>0$.\n\nIf $X$ is
smooth projective over the algebraic closure $k$ of finite field\, and d
oes not have non-trivial differential forms\, one may ask whether all conv
ergent isocrystals have finite monodromy. This is true if $X$ lifts to $W(
k)$. If $X$ lifts to $W_2(k)$\, one can show that stable rank $2$ connect
ions of degree $0$ have finite monodromy (i.e. are trivializable by a fini
te étale cover).\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Dotto (Chicago)
DTSTART;VALUE=DATE-TIME:20210422T150000Z
DTEND;VALUE=DATE-TIME:20210422T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/42
DESCRIPTION:Title: Mod p Bernstein centres of p-adic groups\nby Andrea Dotto (Chicago) a
s part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstrac
t\nThe centre of the category of smooth mod p representations of a p-adic
reductive group does not distinguish the blocks of finite length represent
ations\, in contrast with Bernstein's theory in characteristic zero. Motiv
ated by this observation and the known connections between the Bernstein c
entre and the local Langlands correspondence in families\, we consider the
case of GL_2(Q_p) and we prove that its category of representations exten
ds to a stack on the Zariski site of a simple geometric object: a chain X
of projective lines\, whose points are in bijection with Paskunas's blocks
. Taking the centre over each open subset we obtain a sheaf of rings on X\
, and we expect the resulting space to be closely related to the Emerton--
Gee stack for 2-dimensional representations of the absolute Galois group o
f Q_p. Joint work in progress with Matthew Emerton and Toby Gee.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timo Richarz (Darmstadt)
DTSTART;VALUE=DATE-TIME:20210506T150000Z
DTEND;VALUE=DATE-TIME:20210506T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/43
DESCRIPTION:Title: A categorical Kunneth formula for Weil sheaves\nby Timo Richarz (Darm
stadt) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\
nAbstract\nDrinfeld’s lemma measures the failure of the Kunneth formula
for the etale fundamental group in positive characteristic $p > 0$ in term
s of equivariance data under partial Frobenii. In the talk\, I explain a s
heaf-theoretic formulation for derived categories of lisse and constructib
le Weil sheaves on schemes. This is joint work in progress with Tamir Hemo
and Jakob Scholbach.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tamiozzo (Imperial)
DTSTART;VALUE=DATE-TIME:20210429T150000Z
DTEND;VALUE=DATE-TIME:20210429T162000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/44
DESCRIPTION:Title: On torsion in the cohomology of Hilbert modular varieties\nby Matteo
Tamiozzo (Imperial) as part of Recent Advances in Modern p-Adic Geometry (
RAMpAGe)\n\n\nAbstract\nWe discuss ongoing joint work with Ana Caraiani co
ncerning vanishing results for the generic part of the cohomology of Hilbe
rt modular varieties. A key ingredient is a comparison of the fibres of th
e Hodge-Tate period maps attached to different quaternionic Shimura variet
ies\, inspired by the description of their Goren-Oort stratification given
by Tian-Xiao.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamir Hemo (Caltech)
DTSTART;VALUE=DATE-TIME:20210527T160000Z
DTEND;VALUE=DATE-TIME:20210527T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/45
DESCRIPTION:Title: Unipotent categorical local Langlands correspondence\nby Tamir Hemo (
Caltech) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
n\nAbstract\nWe formulate a categorical form of the local Langlands conjec
ture\nthrough perfect algebraic geometry on a certain infinite dimensional
\nstack classifying F-iscocrystals with additional structure\, analogous t
o\na conjecture made by Fargues-Scholze. Using the categorical trace\ncons
truction we obtain the “unipotent part” of the conjecture from\nBezruk
avnikov’s equivalence of two realizations of the affine Hecke\ncategory.
Joint work in progress with Xinwen Zhu.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Morra (Paris 13)
DTSTART;VALUE=DATE-TIME:20210610T160000Z
DTEND;VALUE=DATE-TIME:20210610T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/46
DESCRIPTION:Title: Moduli of Fontaine–Laffaille modules and local–global compatibility m
od p\nby Stefano Morra (Paris 13) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThe mod $p$-local Langlands prog
ram generated from the observation that certain invariants\non local Galoi
s deformation rings can be predicted by the mod $p$ representation theory
of $p$-adic $\\mathbf{GL}_n$. A first attempt to give evidence for this pr
ogram is in the expected local–global compatibility\, namely that the co
rrespondence will be realized in Hecke eigenspaces of the cohomology of lo
cally symmetric spaces with infinite level at p. In this talk we prove one
direction of this expectation\, namely that the smooth $\\mathbf{GL}_n(\\
mathbb{Q}_{p^f})$ action on Hecke eigenspaces\nin the mod $p$ cohomology o
f compact unitary groups with infinite level at $p$ determines the\nlocal
Galois parameter at $p$-adic places\, when the latter parameters are Fonta
ine–Laffaille.\nThis is joint work in progress with D. Le\, B. Le Hung\,
C. Park and Z. Qian.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mantovan (Caltech)
DTSTART;VALUE=DATE-TIME:20210603T160000Z
DTEND;VALUE=DATE-TIME:20210603T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/47
DESCRIPTION:Title: Infinitely many primes of basic reduction\nby Elena Mantovan (Caltech
) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbst
ract\nIn 1987\, Elkies proved that an elliptic curve defined over the fiel
d of\nrational numbers has infinitely many primes of supersingular reducti
on.\nI will discuss a generalization of this result to the case of special
\ncyclic covers of the projective line ramified at 4 points.\nThis talk is
based on joint work in progress with Wanlin Li\, Rachel\nPries and Yunqi
ng Tang.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Youcis (IMPAN)
DTSTART;VALUE=DATE-TIME:20210513T160000Z
DTEND;VALUE=DATE-TIME:20210513T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/48
DESCRIPTION:Title: Geometric coverings of rigid spaces\nby Alex Youcis (IMPAN) as part o
f Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nFrom
Tate's uniformization of elliptic curves onwards\, the notion of 'covering
space'\, and consequently the notion of fundamental groups\, has played a
guiding role in the development of rigid geometry. A huge leap forward in
our understanding of what exactly covering space/fundamental group might
mean in this context was carried out by de Jong in the mid 90s where he wa
s able to form a fundamental group that encompassed both the topological c
overings (e.g. those appear in Tate's uniformization) and finite etale cov
erings. In our current work we propose an extension of those covering spac
es considered by de Jong\, which not only provides a more conceptual frame
work for talking about covering spaces as a whole\, but also is closed und
er many of the natural geometric operations that de Jong's covering spaces
are not (e.g. disjoint unions and etale localization). Along the way we a
ddress some questions posed in de Jong's article\, as well as giving a con
crete description of the locally constant sheaves in the pro-etale topolog
y which appears in Scholze's work on p-adic Hodge theory.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schraen (Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210624T160000Z
DTEND;VALUE=DATE-TIME:20210624T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/49
DESCRIPTION:Title: Finite length for cohomological mod p representations of GL2 of a p-adic
field\nby Benjamin Schraen (Paris-Saclay) as part of Recent Advances i
n Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nIn the search for a mod
p local Langlands correspondence\, it\nis natural to study the representat
ions of GL2 of a p-adic field F in\nthe mod p cohomology of Shimura curves
. It is expected that the action\nof GL2(F) on a Galois-isotypic subspace
of the mod p cohomology of a\ntower of Shimura curves (of fixed tame level
) has finite length and is\nrelated to the local Galois representation at
p. In the case of modular\ncurves\, this is known by the local-global comp
atibility theorem of\nEmerton. I'll explain how to prove some new cases of
the finiteness of\nthe length when F is an unramified extension of Qp. Th
is finiteness is\nrelated to the computation of the Gelfand-Kirillov dimen
sion of these\nrepresentations. This is a joint work with Christophe Breui
l\, Florian\nHerzig\, Yongquan Hu and Stefano Morra.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART;VALUE=DATE-TIME:20211005T160000Z
DTEND;VALUE=DATE-TIME:20211005T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/50
DESCRIPTION:Title: Bun_G minicourse: Introduction\nby Jared Weinstein (Boston Universit
y) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbs
tract\nThis talk is the first part of a six-part series "$\\mathrm{Bun}_G$
\, Shtukas\, and the Local Langlands Program"\, held Tuesdays and Thursday
s between 5 and 21 October\, 2021.\n\nRecordings and slides will appear he
re: https://sites.google.com/view/rampageseminar/home\n\nSeries abstract:
The recent manuscript of Fargues-Scholze aims to "geometrize" the Langla
nds program for a p-adic group $G$\, by relating the players in that story
to the stack $\\mathrm{Bun}_G$. Following a strategy of V. Lafforgue\, t
he main result of [FS] is the construction of an L-parameter attached to a
smooth irreducible representation of $G$.\n\nThe goal of this series is t
o review the main ideas of this work\, and to discuss two related results:
progress on the Kottwitz conjecture for local shtuka spaces by Hansen-Ka
letha-Weinstein\, and the construction of eigensheaves on $\\mathrm{Bun}_
G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTalk abstract: We wi
ll give a historically motivated introduction to the story\, reviewing mod
uli spaces of $p$-divisible groups\, the Fargues-Fontaine curve\, and the
stack $\\mathrm{Bun}_G$ of $G$-bundles on it. We will then define the mod
uli spaces of local shtukas\, and state our result on their cohomology.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211007T160000Z
DTEND;VALUE=DATE-TIME:20211007T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/51
DESCRIPTION:Title: Bun_G minicourse: Local Langlands\nby Tasho Kaletha (University of M
ichigan) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
n\nAbstract\nThis talk is the second part of a six-part series "$\\mathrm{
Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tuesdays and T
hursdays between 5 and 21 October\, 2021.\n\nRecordings and slides will ap
pear here: https://sites.google.com/view/rampageseminar/home\n\nSeries ab
stract: The recent manuscript of Fargues-Scholze aims to "geometrize" the
Langlands program for a p-adic group $G$\, by relating the players in tha
t story to the stack $\\mathrm{Bun}_G$. Following a strategy of V. Laffor
gue\, the main result of [FS] is the construction of an L-parameter attach
ed to a smooth irreducible representation of $G$.\n\nThe goal of this seri
es is to review the main ideas of this work\, and to discuss two related r
esults: progress on the Kottwitz conjecture for local shtuka spaces by Ha
nsen-Kaletha-Weinstein\, and the construction of eigensheaves on $\\mathr
m{Bun}_G$ when $G=\\mathrm{GL}_n$. \n\nTalk abstract: We will review some
representation-theoretic inputs to HKW. We’ll begin with reviewing the s
tatements of the basic and refined local Langlands correspondence and the
status of their proofs. We will then define the relative position of two m
embers of a compound L-packet\, which is an input to the Kottwitz conjectu
re\, and the relative position of two regular semi-simple elements in inne
r forms. Based on the latter\, we will define a Hecke transfer operator th
at transfers conjugation-invariant functions between inner forms\, and dis
cuss its effect on characters of supercuspidal representations.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART;VALUE=DATE-TIME:20211012T160000Z
DTEND;VALUE=DATE-TIME:20211012T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/52
DESCRIPTION:Title: Bun_G minicourse: Lefschetz formula for diamonds\nby Jared Weinstein
(Boston University) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nThis talk is the third part of a six-part series
"$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tue
sdays and Thursdays between 5 and 21 October\, 2021.\n\nSeries abstract:
The recent manuscript of Fargues-Scholze aims to "geometrize" the Langland
s program for a p-adic group $G$\, by relating the players in that story t
o the stack $\\mathrm{Bun}_G$. Following a strategy of V. Lafforgue\, the
main result of [FS] is the construction of an L-parameter attached to a s
mooth irreducible representation of $G$.\n\nThe goal of this series is to
review the main ideas of this work\, and to discuss two related results:
progress on the Kottwitz conjecture for local shtuka spaces by Hansen-Kale
tha-Weinstein\, and the construction of eigensheaves on $\\mathrm{Bun}_G$
when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTalk abstract: In this
talk we will discuss a very general form of the Lefschetz-Verdier trace f
ormula which applies to stacks (both of schemes and of diamonds). As an a
pplication\, we will show that if a locally pro-$p$ group $G$ acts on a pr
oper diamond $X$\, and if $A$ is a $G$-equivariant $\\ell$-adic sheaf on $
X$ which is "dualizable" (= universally locally acyclic)\, then the cohomo
logy $R\\Gamma(X\,A)$ is an admissible representation of $G$\, whose Haris
h-Chandra distribution can be computed in terms of local terms living on t
he fixed-point locus of $G$ on $X$.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max Planck Institute for Mathematics)
DTSTART;VALUE=DATE-TIME:20211014T160000Z
DTEND;VALUE=DATE-TIME:20211014T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/53
DESCRIPTION:Title: Bun_G minicourse: The Kottwitz conjecture\nby David Hansen (Max Plan
ck Institute for Mathematics) as part of Recent Advances in Modern p-Adic
Geometry (RAMpAGe)\n\n\nAbstract\nThis talk is the fourth part of a six-pa
rt series "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\
, held Tuesdays and Thursdays between 5 and 21 October\, 2021.\n\nRecordin
gs and slides will appear here: https://sites.google.com/view/rampagesemi
nar/home\n\nSeries abstract: The recent manuscript of Fargues-Scholze aim
s to "geometrize" the Langlands program for a p-adic group $G$\, by relati
ng the players in that story to the stack $\\mathrm{Bun}_G$. Following a
strategy of V. Lafforgue\, the main result of [FS] is the construction of
an L-parameter attached to a smooth irreducible representation of $G$.\n\n
The goal of this series is to review the main ideas of this work\, and to
discuss two related results: progress on the Kottwitz conjecture for loca
l shtuka spaces by Hansen-Kaletha-Weinstein\, and the construction of eig
ensheaves on $\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bra
s. \n\nTalk abstract: In this lecture\, we will give a detailed sketch of
the proof of the main theorem of [HKW]\, building on the material in the f
irst three lectures. The idea that the Kottwitz conjecture should follow
from some form of the Lefschetz trace formula goes back to Harris in the '
90s. We will try to emphasize the new ingredients which allow us to implem
ent this idea in full generality.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Anschütz (University of Bonn)
DTSTART;VALUE=DATE-TIME:20211019T160000Z
DTEND;VALUE=DATE-TIME:20211019T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/54
DESCRIPTION:Title: Bun_G minicourse: The spectral action\nby Johannes Anschütz (Univer
sity of Bonn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAG
e)\n\n\nAbstract\nThis talk is the fifth part of a six-part series "$\\mat
hrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tuesdays a
nd Thursdays between 5 and 21 October\, 2021.\n\nRecordings and slides wil
l appear here: https://sites.google.com/view/rampageseminar/home\n\nSerie
s abstract: The recent manuscript of Fargues-Scholze aims to "geometrize"
the Langlands program for a p-adic group $G$\, by relating the players in
that story to the stack $\\mathrm{Bun}_G$. Following a strategy of V. La
fforgue\, the main result of [FS] is the construction of an L-parameter at
tached to a smooth irreducible representation of $G$.\n\nThe goal of this
series is to review the main ideas of this work\, and to discuss two relat
ed results: progress on the Kottwitz conjecture for local shtuka spaces b
y Hansen-Kaletha-Weinstein\, and the construction of eigensheaves on $\\m
athrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTalk abstr
act: In these last two talks\, the Galois group finally enters the picture
. Let $E$ be a local field and a reductive group $G$ over $E$. Following D
at-Helm-Kurinczuk-Moss\, Zhu and Fargues-Scholze\, we will first explain h
ow to construct the \\textit{stack of $L$-parameters}\, which is an ind-Ar
tin-stack parametrizing $\\hat{G}$-valued continuous representations of th
e Weil group of $E$ (for simplicity\, we will restrict our attention to ch
aracteristic zero coefficients). Then we will explain how to construct an
action (called the \\textit{spectral action}) of the category of perfect c
omplexes on the stack of $L$-parameters on the derived category of $\\ell$
-adic sheaves on $\\mathrm{Bun}_G$. This is the main result of Fargues-Sch
olze and is obtained by combining the general version of the geometric Sat
ake equivalence with a presentation of this category of perfect complexes
by generators and relations.\nThe existence of the spectral action allows
one to go from the « automorphic side » to the « Galois side »\, and c
onversely. In one direction\, we will see that it implies quite directly t
he construction of $L$-parameters attached to smooth irreducible represent
ations of $G(E)$. In the other direction\, Fargues formulated in 2014 a st
riking conjecture predicting that one can attach to a discrete $L$-paramet
er an \\textit{Hecke eigensheaf} on $\\mathrm{Bun}_G$ with nice properties
. We will recall what this conjecture says when $G=GL_n$\, and explain how
to prove it when the parameter is assumed to be irreducible\, by using th
e spectral action together with the results of the previous talks.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-César Le Bras (University of Paris 13)
DTSTART;VALUE=DATE-TIME:20211021T160000Z
DTEND;VALUE=DATE-TIME:20211021T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/55
DESCRIPTION:Title: Bun_G minicourse: Construction of the eigensheaf\nby Arthur-César L
e Bras (University of Paris 13) as part of Recent Advances in Modern p-Adi
c Geometry (RAMpAGe)\n\n\nAbstract\nThis talk is the sixth part of a six-p
art series "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"
\, held Tuesdays and Thursdays between 5 and 21 October\, 2021.\n\nRecordi
ngs and slides will appear here: https://sites.google.com/view/rampagesem
inar/home\n\nSeries abstract: The recent manuscript of Fargues-Scholze ai
ms to "geometrize" the Langlands program for a p-adic group $G$\, by relat
ing the players in that story to the stack $\\mathrm{Bun}_G$. Following a
strategy of V. Lafforgue\, the main result of [FS] is the construction of
an L-parameter attached to a smooth irreducible representation of $G$.\n\
nThe goal of this series is to review the main ideas of this work\, and to
discuss two related results: progress on the Kottwitz conjecture for loc
al shtuka spaces by Hansen-Kaletha-Weinstein\, and the construction of ei
gensheaves on $\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Br
as. \n\nTalk abstract: In these last two talks\, the Galois group finally
enters the picture. Let $E$ be a local field and a reductive group $G$ ove
r $E$. Following Dat-Helm-Kurinczuk-Moss\, Zhu and Fargues-Scholze\, we wi
ll first explain how to construct the \\textit{stack of $L$-parameters}\,
which is an ind-Artin-stack parametrizing $\\hat{G}$-valued continuous rep
resentations of the Weil group of $E$ (for simplicity\, we will restrict o
ur attention to characteristic zero coefficients). Then we will explain ho
w to construct an action (called the \\textit{spectral action}) of the cat
egory of perfect complexes on the stack of $L$-parameters on the derived c
ategory of $\\ell$-adic sheaves on $\\mathrm{Bun}_G$. This is the main res
ult of Fargues-Scholze and is obtained by combining the general version of
the geometric Satake equivalence with a presentation of this category of
perfect complexes by generators and relations.\nThe existence of the spect
ral action allows one to go from the « automorphic side » to the « Galo
is side »\, and conversely. In one direction\, we will see that it implie
s quite directly the construction of $L$-parameters attached to smooth irr
educible representations of $G(E)$. In the other direction\, Fargues formu
lated in 2014 a striking conjecture predicting that one can attach to a di
screte $L$-parameter an \\textit{Hecke eigensheaf} on $\\mathrm{Bun}_G$ wi
th nice properties. We will recall what this conjecture says when $G=GL_n$
\, and explain how to prove it when the parameter is assumed to be irreduc
ible\, by using the spectral action together with the results of the previ
ous talks.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART;VALUE=DATE-TIME:20211104T160000Z
DTEND;VALUE=DATE-TIME:20211104T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/56
DESCRIPTION:Title: On the $\\mathbb{Z}_p(i)$ of Bhatt-Morrow-Scholze\nby Akhil Mathew (U
niversity of Chicago) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nI will explain a description of the $\\mathbb{Z}
_p(i)$ complexes defined\nby Bhatt-Morrow-Scholze\, as an integral refinem
ent of\nFontaine-Messing syntomic cohomology\, on a class of $p$-adic form
al\nschemes (including regular noetherian ones and formally smooth schemes
\nover perfectoids) satisfying the "Segal conjecture". This extends a\nnum
ber of comparison results in the literature. Joint with Bhargav\nBhatt.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Kisin (Harvard University)
DTSTART;VALUE=DATE-TIME:20211111T180000Z
DTEND;VALUE=DATE-TIME:20211111T192000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/58
DESCRIPTION:Title: Essential dimension via prismatic cohomology\nby Mark Kisin (Harvard
University) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)
\n\n\nAbstract\nLet $f\\colon Y→X$ be a finite covering map of complex a
lgebraic varieties. The essential dimension of f is the smallest integer e
such that\, birationally\, $f$ arises as the pullback of a covering $Y′
→X′$ of dimension $e$\, via a map $X→X′$. This invariant goes back
to classical questions about reducing the number of parameters in a solut
ion to a general nth degree polynomial\, and appeared in work of Kronecker
and Klein on solutions of the quintic. \n\nI will report on joint work wi
th Benson Farb and Jesse Wolfson\, where we introduce a new technique\, us
ing prismatic cohomology\, to obtain lower bounds on the essential dimensi
on of certain coverings. For example\, we show that for an abelian variety
$A$ of dimension $g$ the multiplication by $p$ map $A→A$ has essential
dimension $g$ for almost all primes $p$.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer & Vincent Pilloni (Orsay)
DTSTART;VALUE=DATE-TIME:20211202T170000Z
DTEND;VALUE=DATE-TIME:20211202T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/59
DESCRIPTION:Title: Higher Coleman Theory I\nby George Boxer & Vincent Pilloni (Orsay) as
part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract
\nWe have developed local cohomology techniques to study the coherent coho
mology of Shimura varieties. The local cohomology groups which appear are
a generalization of overconvergent modular forms studied by Coleman and ma
ny others. \n\nTentative plan of the lectures : \n1) Overview of the resul
ts and analogy with classical representation theory \n2) Definition of the
local cohomology\, vanishing theorems and slope estimates. \n3) Eigenvari
eties and applications.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer & Vincent Pilloni (Orsay)
DTSTART;VALUE=DATE-TIME:20211209T170000Z
DTEND;VALUE=DATE-TIME:20211209T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/60
DESCRIPTION:Title: Higher Coleman Theory II\nby George Boxer & Vincent Pilloni (Orsay) a
s part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstrac
t\nWe have developed local cohomology techniques to study the coherent coh
omology of Shimura varieties. The local cohomology groups which appear are
a generalization of overconvergent modular forms studied by Coleman and m
any others. \n\nTentative plan of the lectures : \n1) Overview of the resu
lts and analogy with classical representation theory \n2) Definition of th
e local cohomology\, vanishing theorems and slope estimates. \n3) Eigenvar
ieties and applications.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer & Vincent Pilloni (Orsay)
DTSTART;VALUE=DATE-TIME:20211216T170000Z
DTEND;VALUE=DATE-TIME:20211216T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/61
DESCRIPTION:Title: Higher Coleman Theory III\nby George Boxer & Vincent Pilloni (Orsay)
as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstra
ct\nWe have developed local cohomology techniques to study the coherent co
homology of Shimura varieties. The local cohomology groups which appear ar
e a generalization of overconvergent modular forms studied by Coleman and
many others. \n\nTentative plan of the lectures : \n1) Overview of the res
ults and analogy with classical representation theory \n2) Definition of t
he local cohomology\, vanishing theorems and slope estimates. \n3) Eigenva
rieties and applications.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Anschütz (Bonn)
DTSTART;VALUE=DATE-TIME:20220202T170000Z
DTEND;VALUE=DATE-TIME:20220202T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/62
DESCRIPTION:Title: On the p-adic theory of local models I\nby Johannes Anschütz (Bonn)
as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstra
ct\nThe first talk concerns the \\'etale cohomology of the v-sheaf local m
odels. After motivating the definition of v-sheaf local models we will det
ermine their special fibers by calculating the nearby cycles of Satake she
aves.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Lourenço (Bonn)
DTSTART;VALUE=DATE-TIME:20220209T170000Z
DTEND;VALUE=DATE-TIME:20220209T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/63
DESCRIPTION:Title: On the p-adic theory of local models II\nby João Lourenço (Bonn) as
part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract
\nThis second talk (based on joint work with Anschütz–Gleason–Richarz
) concerns the Scholze–Weinstein conjecture on the representability of v
-sheaf local models for geometric conjugacy classes of minuscule coweights
. I'll start by reviewing previously known instances of local models in PE
L cases by Rapoport–Zink\, and also via power series Grassmannians by Pa
ppas–Zhu. I'll briefly explain how to slightly refine the latter (joint
with Fakhruddin–Haines–Richarz). Building on this\, I'll explain the c
omparison of p-adic admissible loci in the Witt Grassmannian with those fo
und in power series Grassmannians. Next\, I'll prove the\nspecialization p
rinciple for sufficiently nice kimberlites\, which include v-sheaf local m
odels (even for non-minuscule cocharacters). Finally\, I'm going to explai
n how to compute the specialization mapping in families\, deducing the Sch
olze–Weinstein conjecture.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (Princeton)
DTSTART;VALUE=DATE-TIME:20220119T170000Z
DTEND;VALUE=DATE-TIME:20220119T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/64
DESCRIPTION:Title: On the p-adic Hodge structure of completed cohomology of modular curves I
\nby Lue Pan (Princeton) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nLet $p$ be a prime. I plan to explain how
to read the $p$-adic Hodge structure of the $p$-adically completed cohomo
logy of modular curves by studying the $p$-adic geometry of the modular cu
rves at infinite level. One main tool is the relative Sen theory (also cal
led $p$-adic Simpson correspondence) which provides a first-order differen
tial equation and allows us to apply differential operators pulled back fr
om the flag variety along the Hodge-Tate period map.\n\nLecture (1): Hodge
-Tate structure\nLecture (2): de Rham structure\n\nIf time permits\, I wil
l also discuss several applications.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (Princeton)
DTSTART;VALUE=DATE-TIME:20220126T170000Z
DTEND;VALUE=DATE-TIME:20220126T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/65
DESCRIPTION:Title: On the p-adic Hodge structure of completed cohomology of modular curves I
I\nby Lue Pan (Princeton) as part of Recent Advances in Modern p-Adic
Geometry (RAMpAGe)\n\n\nAbstract\nLet $p$ be a prime. I plan to explain ho
w to read the $p$-adic Hodge structure of the $p$-adically completed cohom
ology of modular curves by studying the $p$-adic geometry of the modular c
urves at infinite level. One main tool is the relative Sen theory (also ca
lled $p$-adic Simpson correspondence) which provides a first-order differe
ntial equation and allows us to apply differential operators pulled back f
rom the flag variety along the Hodge-Tate period map.\n\nLecture (1): Hodg
e-Tate structure\nLecture (2): de Rham structure\n\nIf time permits\, I wi
ll also discuss several applications.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jackson Morrow (Berkeley)
DTSTART;VALUE=DATE-TIME:20220302T170000Z
DTEND;VALUE=DATE-TIME:20220302T182000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/66
DESCRIPTION:Title: On p-adic uniformization of abelian varieties with good reduction\nby
Jackson Morrow (Berkeley) as part of Recent Advances in Modern p-Adic Geo
metry (RAMpAGe)\n\n\nAbstract\nInvestigating the p-adic integration map co
nstructed by J.-M. Fontaine during the 90's\, which is the main tool for p
roving the Hodge--Tate decomposition of the Tate module of an abelian vari
ety over a p-adic field\, we realized that the group of p-adic points of t
he above-named abelian variety\, satisfying certain hypothesis\, has a typ
e of p-adic uniformization which was not remarked before. This is joint wo
rk with A. Iovita and A. Zaharescu.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyan Daniel Li-Huerta (Harvard)
DTSTART;VALUE=DATE-TIME:20220323T160000Z
DTEND;VALUE=DATE-TIME:20220323T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/67
DESCRIPTION:Title: The plectic conjecture over local fields\nby Siyan Daniel Li-Huerta (
Harvard) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
n\nAbstract\nThe étale cohomology of varieties over $\\mathbf{Q}$ enjoys
a Galois action. In the case of Hilbert modular varieties\, Nekovář-Scho
ll observed that this Galois action on the level of cohomology extends to
a much larger profinite group: the plectic group. They conjectured that th
is extension holds even on the level of complexes\, as well as for more ge
neral Shimura varieties.\n\nWe present a proof of the analogue of this con
jecture for local Shimura varieties. This implies that\, for p-adically un
iformized global Shimura varieties\, we obtain an action of the local plec
tic group on the level of complexes. The proof crucially uses Fargues–Sc
holze's results on the cohomology of moduli spaces of local shtukas.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Johansson (Chalmers/Gothenburg)
DTSTART;VALUE=DATE-TIME:20220504T160000Z
DTEND;VALUE=DATE-TIME:20220504T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/68
DESCRIPTION:Title: Signs of a p-adic geometric Langlands correspondence: part I\nby Chri
stian Johansson (Chalmers/Gothenburg) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nRecent developments in the geome
trization of local Langlands correspondence suggests\, among other things\
, that the category of smooth complex representations of a p-adic group ca
n be embedded fully faithfully into a category of ind-coherent sheaves on
a moduli space of Weil-Deligne representations. For the p-adic local Langl
ands correspondence\, a geometric perspective is more speculative. In thes
e talks we will outline the construction of a fully faithful contravariant
embedding of the category of p-adic locally admissible representations of
GL(2\,Qp) into a suitable category of coherent sheaves on the moduli stac
k of 2-dimensional p-adic representations of Gal(Qp-bar/Qp)\, constructed
by Wang-Erickson. We will also discuss analogous statements for SL(2\,Qp)\
, highlighting the role of endoscopy.\n\n\nThis is joint work between Chri
stian Johansson\, James Newton and Carl Wang-Erickson.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (University of Michigan)
DTSTART;VALUE=DATE-TIME:20220518T160000Z
DTEND;VALUE=DATE-TIME:20220518T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/70
DESCRIPTION:Title: u-torsions in Breuil-Kisin prismatic cohomology\nby Shizhang Li (Univ
ersity of Michigan) as part of Recent Advances in Modern p-Adic Geometry (
RAMpAGe)\n\n\nAbstract\nI shall report a joint work with Tong Liu\, in whi
ch we discuss a tiny piece of the Breuil--Kisin prismatic cohomology modul
e of a general smooth proper scheme X over a p-adic ring of integers O_K.
I will try to explain why this tiny piece can be interesting from both alg
ebro-gemetric and number-theoretic point of views. Also planned is a concr
ete description of an interesting example extracted from the work of Bhatt
--Morrow--Scholze\, giving rise to an example negating a prediction that B
reuil made some 20 years ago.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Wang-Erickson (University of Pittsburgh)
DTSTART;VALUE=DATE-TIME:20220525T160000Z
DTEND;VALUE=DATE-TIME:20220525T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/71
DESCRIPTION:Title: Signs of a p-adic geometric Langlands correspondence: part II\nby Car
l Wang-Erickson (University of Pittsburgh) as part of Recent Advances in M
odern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nRecent developments in the
geometrization of local Langlands correspondence suggests\, among other th
ings\, that the category of smooth complex representations of a $p$-adic g
roup can be embedded fully faithfully into a category of ind-coherent shea
ves on a moduli space of Weil-Deligne representations. For the $p$-adic lo
cal Langlands correspondence\, a geometric perspective is more speculative
. In these talks we will outline the construction of a fully faithful cont
ravariant embedding of the category of $p$-adic locally admissible represe
ntations of $\\mathrm{GL}(2\,\\mathbb{Q}_p)$ into a suitable category of c
oherent sheaves on the moduli stack of 2-dimensional $p$-adic representati
ons of $\\mathrm{Gal}(\\overline{\\mathbb{Q}_p}/\\mathbb{Q}_p)$. In this s
econd talk in particular\, we will emphasize the explicit and computable n
ature of the moduli stack of Galois representations and certain sheaves on
it.\n\nAttendance at the prior talk in this series will not be presumed.\
n\nThis is joint work between Christian Johansson\, James Newton and Carl
Wang-Erickson.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Esteban Rodriguez Camargo (Ecole Normale Supérieure de Lyon)
DTSTART;VALUE=DATE-TIME:20220601T160000Z
DTEND;VALUE=DATE-TIME:20220601T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/72
DESCRIPTION:Title: Solid locally analytic representations of $p$-adic Lie groups\nby Jua
n Esteban Rodriguez Camargo (Ecole Normale Supérieure de Lyon) as part of
Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nMotiva
ted from the works of Lazard\, Schneider-Teitelbaum and Emerton\, and from
the theory of condensed mathematics developed by Clausen and Scholze\, we
give new foundations for the theory of locally analytic representations o
f (compact) $p$-adic Lie groups. In this talk we will discuss how the inte
rpretation of taking analytic vectors à la Emerton shows that the concept
of being an analytic representation for some open compact subgroup is the
same as being a module over some analytic distribution algebra. This obse
rvation algebraizes the theory of locally analytic representations\, and s
ome comparison theorems of Lazard and Tamme on continuous - locally anal
ytic - Lie algebra cohomology hold for general solid representations by b
asic homological algebra arguments. Joint work with Joaquín Rodrigues Jac
into.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhargav Bhatt (IAS/Princeton)
DTSTART;VALUE=DATE-TIME:20220810T160000Z
DTEND;VALUE=DATE-TIME:20220810T172000Z
DTSTAMP;VALUE=DATE-TIME:20240224T070455Z
UID:RAMpAGe/73
DESCRIPTION:Title: Prismatic F-gauges (final RAMpAGe talk!)\nby Bhargav Bhatt (IAS/Princ
eton) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\n
Abstract\nRecording: https://bostonu.zoom.us/rec/share/DzQW6dw2X-T8Rhqlth
oGxAO0kD4hYmOKebIh8nFxnRh9U-rz15TrtPG2KgSuz3zZ.YaFrVJvWNFbn6xLV\n\nNotes:
https://drive.google.com/file/d/1PWW_guqKGBvWsrnddjX18XdTKX2KbeLG/view?usp
=sharing\n\nPrismatic F-gauges are the natural coefficient systems for pri
smatic cohomology\, analogous to variations of Hodge structures in classic
al Hodge theory. This talk will describe a couple of equivalent perspectiv
es on this notion\, and then present evidence suggesting that prismatic F-
gauges over Spf(Z_p) might provide a meaningful notion of crystallinity fo
r representations of the absolute Galois group of Q_p with torsion coeffic
ients. This is joint work in progress with Jacob Lurie\, building on work
of Drinfeld.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/73/
END:VEVENT
END:VCALENDAR