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BEGIN:VEVENT
SUMMARY:David Stewart (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20200515T150000Z
DTEND;VALUE=DATE-TIME:20200515T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/1
DESCRIPTION:Title: Irreducible modules for pseudo-reductive groups\nby David Stew
art (University of Newcastle) as part of Quadratic forms\, linear algebrai
c groups and beyond\n\n\nAbstract\n(Jt with Michael Bate) For any smooth c
onnected group G over an arbitrary field k\, its irreducible modules are i
n 1-1 correspondence with those of the pseudo-reductive quotient G/R_{u\,k
}(G) where R_{u\,k}(G) is the k-defined unipotent radical of G. If k is im
perfect\, a pseudo-reductive group may not be reductive. That means that o
ver the algebraic closure of k\, one sees some unipotent radical which is
not visible over k. If G has a split maximal torus\, much of the theory of
split reductive groups carries over and we give dimension formulae for ir
reducible G-modules which reduce the study to the split reductive case and
commutative pseudo-reductive case.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Duncan (University of South Carolina)
DTSTART;VALUE=DATE-TIME:20200522T150000Z
DTEND;VALUE=DATE-TIME:20200522T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/2
DESCRIPTION:Title: Cohomological invariants and separable algebras\nby Alexander
Duncan (University of South Carolina) as part of Quadratic forms\, linear
algebraic groups and beyond\n\n\nAbstract\nA separable algebra over a fiel
d k is a finite direct sum of central simple algebras over finite separabl
e extensions of k. It is natural to attach separable algebras to k-forms o
f algebraic objects. The fundamental example is the central simple algebra
corresponding to a Severi-Brauer variety. Blunk considered a pair of Azum
aya algebras attached to a del Pezzo surface of degree 6. More generally\,
one can consider endomorphism algebras of exceptional objects in derived
categories. Alternatively\, one can view these constructions as cohomologi
cal invariants of degree 2 with values in quasitrivial tori.\n\nIn the cas
e of Severi-Brauer varieties and Blunk's example of del Pezzo surfaces of
degree 6\, these invariants suffice to completely determine the isomorphis
m classes of the underlying objects. However\, in general they are not suf
ficient. We characterize which k-forms can be distinguished from one anoth
er using the theory of coflasque resolutions of reductive algebraic groups
. Moreover\, we discuss connections to rationality questions and to the Ta
te-Shafarevich group for number fields. \n\nThis is based on joint work wi
th Matthew Ballard\, Alicia Lamarche\, and Patrick McFaddin.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20200529T150000Z
DTEND;VALUE=DATE-TIME:20200529T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/3
DESCRIPTION:Title: Codimension two cycles on classifying stacks of algebraic tori
\nby Federico Scavia (University of British Columbia) as part of Quadratic
forms\, linear algebraic groups and beyond\n\n\nAbstract\nWe give an exam
ple of an algebraic torus $T$ such that the group ${\\rm CH}^2(BT)_{\\rm t
ors}$ is non-trivial. This answers a question of Blinstein and Merkurjev.\
n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danny Krashen (Rutgers University)
DTSTART;VALUE=DATE-TIME:20200605T150000Z
DTEND;VALUE=DATE-TIME:20200605T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/4
DESCRIPTION:Title: Field patching\, local-global principles and rationality\nby D
anny Krashen (Rutgers University) as part of Quadratic forms\, linear alge
braic groups and beyond\n\n\nAbstract\nThis talk will describe local-globa
l principles for torsors for algebraic groups over a semiglobal field - th
at is\, a one variable function field over a complete discretely valued fi
eld.\nIn particular\, I will describe recent joint work with Colliot-Thél
ène\, Harbater\, Hartmann\, Parimala and Suresh in which we connect this
question in certain cases to questions of R-equivalence for the group\, an
d in some cases are able to give finiteness results and combinatorial desc
riptions for the obstruction to local-global principles.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Pirisi (KTH Royal Institute of Technology)
DTSTART;VALUE=DATE-TIME:20200612T150000Z
DTEND;VALUE=DATE-TIME:20200612T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/5
DESCRIPTION:Title: Brauer groups of moduli of hyperelliptic curves\, via cohomologica
l invariants\nby Roberto Pirisi (KTH Royal Institute of Technology) as
part of Quadratic forms\, linear algebraic groups and beyond\n\n\nAbstrac
t\nGiven an algebraic variety X\, the Brauer group of X is the group of Az
umaya algebras over X\, or equivalently the group of Severi-Brauer varieti
es over X\, i.e. fibrations over X which are étale locally isomorphic to
a projective space. It was first studied in the case where X is the spectr
um of a field by Noether and Brauer\, and has since became a central objec
t in algebraic and arithmetic geometry\, being for example one of the firs
t obstructions to rationality used to produce counterexamples to Noether's
problem of whether given a representation V of a finite group G the quoti
ent V/G is rational. While the Brauer group has been widely studied for sc
hemes\, computations at the level of moduli stacks are relatively recent\,
the most prominent of them being the computations by Antieau and Meier of
the Brauer group of the moduli stack of elliptic curves over a variety of
bases\, including Z\, Q\, and finite fields.\nIn a recent joint work with
A. Di Lorenzo\, we use the theory of cohomological invariants\, and its e
xtension to algebraic stacks\, to completely describe the Brauer group of
the moduli stacks of hyperelliptic curves over fields of characteristic ze
ro\, and the prime-to-char(k) part in positive characteristic. It turns ou
t that the (non-trivial part of the) group is generated by cyclic algebras
\, by an element coming from a map to the classifying stack of étale alge
bras of degree 2g+2\, and when g is odd by the Brauer-Severi fibration ind
uced by taking the quotient of the universal curve by the hyperelliptic in
volution. This paints a richer picture than in the case of elliptic curves
\, where all non-trivial elements come from cyclic algebras.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maike Gruchot (University of Aachen)
DTSTART;VALUE=DATE-TIME:20200619T150000Z
DTEND;VALUE=DATE-TIME:20200619T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/6
DESCRIPTION:Title: Variations of G-complete reducibility\nby Maike Gruchot (Unive
rsity of Aachen) as part of Quadratic forms\, linear algebraic groups and
beyond\n\n\nAbstract\nIn this talk we discuss variations of Serre’s noti
on of complete reducibility. Let $G$ be reductive algebraic group and $K$
be a reductive subgroup. First we consider a relative version in the case
of a subgroup of the $G$ which normalizes the identity component $K^0$ of
$K$. It turns that such a subgroup is relatively $G$-completely reducible
with respect to $K$ if and only if its image in the automorphism group of
$K^0$ is completely reducible. This allows us to generalize a number of fu
ndamental results from the absolute to the relative setting.\nBy results o
f Serre and Bate–Martin–Röhrle\, the usual notion of $G$-complete red
ucibility can be re-framed as a property of an action of a group on the sp
herical building of the identity component of $G$. We discuss that other v
ariations of this notion\, such as relative complete reducibility and σ-c
omplete reducibility which can also be viewed as special cases of this bui
lding-theoretic definition.\nThis is based on joint work with A. Litterick
and G. Röhrle.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART;VALUE=DATE-TIME:20200626T150000Z
DTEND;VALUE=DATE-TIME:20200626T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/7
DESCRIPTION:Title: Cohomological invariants in positive characteristic\nby Burt T
otaro (UCLA) as part of Quadratic forms\, linear algebraic groups and beyo
nd\n\n\nAbstract\nWe determine the mod p cohomological invariants for seve
ral affine group schemes G in chararacteristic p. These are invariants of
G-torsors with values in etale motivic cohomology\, or equivalently in Kat
o's version of Galois cohomology based on differential forms. In particula
r\, we find the mod 2 cohomological invariants for the symmetric groups an
d the orthogonal groups in characteristic 2\, which Serre computed in char
acteristic not 2.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benedict Williams (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20200710T150000Z
DTEND;VALUE=DATE-TIME:20200710T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/8
DESCRIPTION:Title: Algebras requiring many generators\nby Benedict Williams (Univ
ersity of British Columbia) as part of Quadratic forms\, linear algebraic
groups and beyond\n\n\nAbstract\nA result of Forster says that if R is a n
oetherian ring of (Krull) dimension d\, then a rank-n projective module ov
er R can be generated by d+n elements\, and results of Chase and Swan impl
y that this bound is sharp—there exist examples that cannot be generated
by fewer than d+n elements. We view "projective modules" as forms of the
most trivial kind of non-unital R-algebra\, i.e.\, where the multiplicatio
n is identically 0. We take the results of Forster\, Chase and Swan as a s
tarting point for investigations into forms of other algebras.\n\nFix a fi
eld k and a k-algebra B\, not assumed unital or commutative. Let G denote
the automorphism group scheme of B as an algebra. Let U_r denote the varie
ty of r-tuples of elements that generate B as a k-algebra. In favourable c
ircumstances\, U_r/G is a k-variety\, generalizing the Grassmannian\, that
classifies forms of the algebra B equipped with r generators. In addition
\, as far as A1-invariant cohomology theories are concerned U_r/G approxim
ates the classifying stack BG. By measuring the non-injectivity of the map
of Chow rings CH(BG)->CH(U_r/G)\, we can produce examples of algebras (ov
er a ring R) requiring many generators\, generalizing the example of Chase
and Swan. I will tell a fuller version of this story\, with emphasis on t
he case where B is a matrix algebra\, so that U_r/G classifies Azumaya alg
ebras with r generators. The majority of the talk concerns joint work with
Uriya First and Zinovy Reichstein\, but I will mention some joint work wi
th Taeuk Nam & Cindy Tan and some independent work of Sebastian Gant.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Chayet (ECAM-EPMI)
DTSTART;VALUE=DATE-TIME:20200703T150000Z
DTEND;VALUE=DATE-TIME:20200703T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/9
DESCRIPTION:Title: E8 and a new class of commutative non-associative algebras with a
continuous Pierce Spectrum\nby Maurice Chayet (ECAM-EPMI) as part of Q
uadratic forms\, linear algebraic groups and beyond\n\n\nAbstract\nT.A. Sp
ringer knew decades ago of the existence of a Group invariant commutative
algebra structure on the 3875 dimensional representation of $E_8$. It was
recently shown by S. Garibaldi and R. Guralnick that the automorphism grou
p of this unique commutative algebra coincides with $E_8$. However a desc
ription of this algebra has been a lingering question\, ever since it was
noticed by T.A. Springer.\n\nIn this talk\, based on joint work with Skip
Garibaldi\, we explain a correspondence which associates to each simple Li
e algebra\, a commutative non associative unital algebra\, and provide an
explicit closed form expression for the product. This correspondence encom
passes the 3875 invariant algebra for $E_8$ via the addition of a unit. Th
ese algebras turn out to be simple and are endowed with a non-degenerate
“associative” bilinear invariant form. Unlike their closet cousins\, t
he Jordan Algebras\, these algebras are not power associative and share th
e unusual property of having the unit interval as part of their Pierce Spe
ctrum.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raman Parimala (Emory University)
DTSTART;VALUE=DATE-TIME:20200914T150000Z
DTEND;VALUE=DATE-TIME:20200914T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/10
DESCRIPTION:Title: A Hasse principle for simply connected groups\nby Raman Parim
ala (Emory University) as part of Quadratic forms\, linear algebraic group
s and beyond\n\n\nAbstract\nKneser proposed a conjecture that if $G$ is a
semi-simple simply connected linear algebraic group defined over a number
field $k$ and $Y$ a principal homogeneous space under $G$\, then $Y$ satis
fies Hasse principle\, i.e.\, $Y$ has a rational point over $k$ if it does
over completions of $k$ at all its places. This is now a theorem due to
Kneser for classical groups\, Harder for exceptional groups of type other
than $E_8$ and Chernousov for groups of type $E_8$. There were questions
and conjectures on similar Hasse principles over function fields of $p$-a
dic curves and more generally\, semi global fields\, i.e.\,\nfunction fiel
ds of curves over complete discrete valued fields\, with respect to all th
eir discrete valuations. We shall discuss recent progress in this directi
on.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Borovoi (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200921T150000Z
DTEND;VALUE=DATE-TIME:20200921T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/11
DESCRIPTION:Title: Galois cohomology of real reductive groups\nby Mikhail Borovo
i (Tel Aviv University) as part of Quadratic forms\, linear algebraic grou
ps and beyond\n\n\nAbstract\nUsing ideas of Kac and Vinberg\, we give a si
mple combinatorial method of computing the Galois cohomology of semisimple
groups over the field $\\mathbb R$ of real numbers. I will explain the me
thod by the examples of simple groups of type $E_7$ (both adjoint and simp
ly connected).\n\nThis is a joint work with Dmitry A. Timashev\, Moscow\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Lourdeaux (University of Lyon)
DTSTART;VALUE=DATE-TIME:20200928T150000Z
DTEND;VALUE=DATE-TIME:20200928T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/12
DESCRIPTION:Title: Brauer invariants of linear algebraic groups\nby Alexandre Lo
urdeaux (University of Lyon) as part of Quadratic forms\, linear algebraic
groups and beyond\n\n\nAbstract\nOur talk deals with the cohomological in
variants of smooth and connected linear algebraic groups over an arbitrary
field. The notion of cohomological invariants was formalized by Serre in
the 90’s. It enables to study via Galois cohomology the geometry of line
ar algebraic groups or forms of algebraic stuctures (such as central simpl
e algebras with involution).\n\nWe intend to introduce the general ideas o
f the theory and to present a generalization of a result by Blinstein and
Merkurjev on degree 2 invariants with coefficients Q/Z(1)\, that is invari
ants taking values in the Brauer group. More precisely our result gives a
description of these invariants for every smooth and connected linear grou
ps\, in particular for non reductive groups over an imperfect field (as ps
eudo-reductive or unipotent groups for instance).\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rapinchuk (Michigan State University)
DTSTART;VALUE=DATE-TIME:20201005T150000Z
DTEND;VALUE=DATE-TIME:20201005T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/13
DESCRIPTION:Title: Algebraic groups with good reduction\nby Igor Rapinchuk (Mich
igan State University) as part of Quadratic forms\, linear algebraic group
s and beyond\n\n\nAbstract\nTechniques involving reduction are very common
in number theory and arithmetic geometry. In particular\, elliptic curves
and general abelian varieties having good reduction have been the subject
of very intensive investigations over the years. The purpose of this talk
is to report on recent work that focuses on good reduction in the context
of reductive linear algebraic groups over finitely generated fields. In a
ddition\, we will highlight some applications to the study of local-global
principles and the analysis of algebraic groups having the same maximal t
ori. (Parts of this work are joint with V. Chernousov and A. Rapinchuk.)\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Merkurjev (UCLA)
DTSTART;VALUE=DATE-TIME:20201012T150000Z
DTEND;VALUE=DATE-TIME:20201012T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/14
DESCRIPTION:Title: Operations in connective K-theory\nby Alexander Merkurjev (UC
LA) as part of Quadratic forms\, linear algebraic groups and beyond\n\n\nA
bstract\nThis is a joint work with A.Vishik. A relation between Chow theor
y and algebraic K-theory of smooth algebraic varieties is given by a ring
homomorphism from the Chow ring to the graded Grothendieck ring of a varie
ty associated with the topological filtration. A much better relation can
be established via connective K-theory that maps to both Chow theory and K
-theory\, so the connective K-theory deserves detailed study.\n\nSteenrod
operations (mod p) and Adams operations are essentially all additive opera
tions in Chow theory and K-theory respectively. In the talk we describe th
e ring of additive operations in connective K-theory.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cyril Demarche (Institut de Mathématiques de Jussieu)
DTSTART;VALUE=DATE-TIME:20201019T150000Z
DTEND;VALUE=DATE-TIME:20201019T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/15
DESCRIPTION:Title: Splitting families in Galois cohomology\nby Cyril Demarche (I
nstitut de Mathématiques de Jussieu) as part of Quadratic forms\, linear
algebraic groups and beyond\n\n\nAbstract\nLet k be a field and A a finite
discrete Galois module. For any integer $n >1$\, let $x$ be a cohomology
class in $H^n(k\, A)$. We show that there exists a countable familiy of (s
mooth\, geometrically integral) $k$-varieties\, such that the following ho
lds: for any field extension $K/k$\, the restriction of $x$ vanishes in $H
^n(K\, A)$ if and only if one of the varieties has an $K$-point. In the ca
se $n= 2$\, we note that one variety (called a splitting variety for $x$)
is enough. The question of the existence of splitting varieties (or splitt
ing families) is insprired by the construction of norm varieties for symbo
ls by Rost. This is joint work with Mathieu Florence.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cameron Ruether (University of Ottawa)
DTSTART;VALUE=DATE-TIME:20201026T150000Z
DTEND;VALUE=DATE-TIME:20201026T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/16
DESCRIPTION:Title: Injections from Kronecker Products and the Cohomological Invarian
ts of Half-Spin\nby Cameron Ruether (University of Ottawa) as part of
Quadratic forms\, linear algebraic groups and beyond\n\n\nAbstract\nLet $G
$ be a linear algebraic group over a field $F$. As introduced by Serre\, d
egree $n$ cohomological invariants of $G$ with coefficients in a group $A$
\, where $A$ is equipped with an action of the absolute Galois group of $F
$\, are natural transformations of Galois cohomology functors $H^1(-\,G) \
\to H^n(-\,A)$. Commonly studied are the degree three invariants with coef
ficients in $\\mathbb{Q}/\\mathbb{Z} \\otimes \\mathbb{Q}/\\mathbb{Z}$. Th
ese invariants were recently described by Merkurjev for the semisimple adj
oint case\, and by Bermudez and Ruozzi for semisimple $G$ which are neithe
r simply connected nor adjoint. In particular\, they described the structu
re of the normalized degree three invariants (those which send the trivial
object to zero) of the half-spin group $\\operatorname{HSpin}_{16}$. By g
eneralizing a technique of Garibaldi we construct new injections into $\\o
peratorname{HSpin}$ induced by the Kronecker tensor product map. In partic
ular we construct an injection $\\operatorname{PSp}_{2n} \\times \\operato
rname{PSp}_2m \\to \\operatorname{HSpin}_{4nm}$ which we use to describe t
he normalized invariants of $\\operatorname{HSpin}_{4k}$ for any $k$\, gen
eralizing the result of Bermudez and Ruozzi.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Stavrova (St. Petersburg University)
DTSTART;VALUE=DATE-TIME:20201102T160000Z
DTEND;VALUE=DATE-TIME:20201102T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/17
DESCRIPTION:Title: Torsors of isotropic reductive groups over Laurent polynomials\nby Anastasia Stavrova (St. Petersburg University) as part of Quadratic
forms\, linear algebraic groups and beyond\n\n\nAbstract\nLet $k$ be a fie
ld of characteristic 0. Let $G$ be a reductive group over the ring of Laur
ent polynomials $R=k[x_1^{\\pm 1}\,\\ldots\,x_n^{\\pm 1}]$. We prove that
$G$ has isotropic rank $\\ge 1$ over $R$ iff it has isotropic rank $\\ge 1
$ over the field of fractions $k(x_1\,\\ldots\,x_n)$ of $R$\, and if this
is the case\, then the natural map $H^1_{et}(R\,G)\\to H^1_{et}(k(x_1\,\\l
dots\,x_n)\,G)$ has trivial kernel and $G$ is loop reductive\, i.e. $G$ co
ntains a maximal $R$-torus. We also deduce that if $G$ is a reductive grou
p over $R$ of isotropic rank $\\ge 2$\, then the natural map of non-stable
$K_1$-functors $K_1^G(R)\\to K_1^G\\bigl( k((x_1))\\ldots ((x_n)) \\bigr)
$ is injective\, and an isomorphism if $G$ is moreover semisimple.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucy Moser-Jauslin (Université de Bourgogne)
DTSTART;VALUE=DATE-TIME:20201109T160000Z
DTEND;VALUE=DATE-TIME:20201109T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/18
DESCRIPTION:Title: Forms of almost homogeneous varieties\nby Lucy Moser-Jauslin
(Université de Bourgogne) as part of Quadratic forms\, linear algebraic g
roups and beyond\n\n\nAbstract\nIn this talk\, we will discuss almost homo
geneous varieties for reductive groups over a perfect field $k$. Let $K$ b
e an algebraic closure of $k$\, and let $G$ be a connected reductive $K$-g
roup with a fixed $k$-form $F$. A normal $G$-variety over $K$ is almost ho
mogeneous if it has an open dense orbit. Given an almost homogeneous $G$-
variety $X$\, the goal of this talk will be to determine $k$-forms of $X$
which are compatible with the $k$-form $F$ of $G$. In order to do this\, w
e describe an action of the Galois group on the combinatorics developed i
n Luna-Vust theory. This is joint work with Ronan Terpereau.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kęstutis Česnavičius (Université Paris-Sud)
DTSTART;VALUE=DATE-TIME:20201116T160000Z
DTEND;VALUE=DATE-TIME:20201116T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/19
DESCRIPTION:Title: Grothendieck–Serre in the split unramified case\nby Kęstut
is Česnavičius (Université Paris-Sud) as part of Quadratic forms\, line
ar algebraic groups and beyond\n\n\nAbstract\nThe Grothendieck–Serre con
jecture predicts that every generically trivial torsor under a reductive g
roup scheme G over a regular local ring R is trivial. We settle it in the
case when G is split and R is unramified. To overcome obstacles that have
so far kept the mixed characteristic case out of reach\, we rely on the re
cently-established Cohen–Macaulay version of the resolution of singulari
ties.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Petrov (St. Petersburg University)
DTSTART;VALUE=DATE-TIME:20201123T160000Z
DTEND;VALUE=DATE-TIME:20201123T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/20
DESCRIPTION:Title: Isotropy of Tits construction\nby Victor Petrov (St. Petersbu
rg University) as part of Quadratic forms\, linear algebraic groups and be
yond\n\n\nAbstract\nTits construction produces a Lie algebra out of a comp
osition algebra and an exceptional Jordan algebra. The type of the result
is $F_4$\, ${}^2E_6$\, $E_7$ or $E_8$ when the composition algebra has dim
ension 1\,2\,4 or 8 respectively. Garibaldi and Petersson noted that the T
its index ${}^2E_6^{35}$ cannot occur as a result of Tits construction. Re
cently Alex Henke proved that the Tits index $E_7^{66}$ is also not possib
le. We push the analogy further and show that Lie algebras of Tits index $
E_8^{133}$ don’t lie in the image of the Tits construction. The proof re
lies on basic facts about symmetric spaces and our joint result with Garib
aldi and Semenov about isotropy of groups of type $E_7$ in terms of the Ro
st invariant. This is a part of a work in progress joint with Simon Rigby.
\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Wertheim (UCLA)
DTSTART;VALUE=DATE-TIME:20201130T160000Z
DTEND;VALUE=DATE-TIME:20201130T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/21
DESCRIPTION:Title: Degree One Milnor K-Invariants of Groups of Multiplicative Type\nby Alex Wertheim (UCLA) as part of Quadratic forms\, linear algebraic
groups and beyond\n\n\nAbstract\nMany important algebraic objects can be v
iewed as $G$-torsors over a field $F$\, where $G$ is an algebraic group ov
er $F$. For example\, there is a natural bijection between $F$-isomorphism
classes of central simple $F$-algebras of degree n and $\\operatorname{PG
L}_n(F)$-torsors over $\\operatorname{Spec}(F)$. Much as one may study pri
ncipal bundles on a manifold via characteristic classes\, one may likewise
study G-torsors over a field via certain associated Galois cohomology cla
sses. This principle is made precise by the notion of a cohomological inva
riant\, which was first introduced by Serre. \n\nIn this talk\, we will de
termine the cohomological invariants for algebraic groups of multiplicativ
e type with values in $H^{1}(-\, Q/Z(1))$. Our main technical analysis wil
l center around a careful examination of $\\mu_n$-torsors over a smooth\,
connected\, reductive algebraic group. Along the way\, we will compute a r
elated group of invariants for smooth\, connected\, reductive groups.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Sechin (University of Regensburg)
DTSTART;VALUE=DATE-TIME:20201207T160000Z
DTEND;VALUE=DATE-TIME:20201207T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/22
DESCRIPTION:Title: Morava K-theory pure motives with applications to quadrics\nb
y Pavel Sechin (University of Regensburg) as part of Quadratic forms\, lin
ear algebraic groups and beyond\n\n\nAbstract\nMorava K-theories $K(n)$ ar
e cohomology theories that have graded fields of positive characteristic a
s coefficient rings and that are obtained from algebraic cobordism of Levi
ne-Morel by change of coefficients. Pure motives with respect to $K(n)$ fi
t in-between Chow motives and $K_0$-motives (with $p$-localized or $p$-tor
sion coefficients)\, e.g. allowing to transfer $K(n)$-decompositions to $K
(m)$-decompositions whenever $m < n$. Thus\, it might be a reasonable appr
oach in the study of motivic decompositions to start with $K(1)$-motives (
i.e. more or less $K_0$-motives) and continue to $K(2)$-\, $K(3)$-motives
and so on\, eventually arriving to Chow-motives.\nOn the other hand we for
mulate a conjectural principle that connects the splitting of $K(n)$-motiv
e. \nwith the triviality of cohomological invariants of degrees less than
$n+1$.\nI plan to outline the proof of this principle for quadrics and exp
lain its consequences \nfor Chow groups of quadrics lying in powers of the
fundamental ideal in the Witt ring.\nThe talk is mostly based on the join
t work with Nikita Semenov.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Primosic (University of Alberta)
DTSTART;VALUE=DATE-TIME:20201214T160000Z
DTEND;VALUE=DATE-TIME:20201214T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/23
DESCRIPTION:Title: Motivic cohomology and infinitesimal group schemes\nby Eric P
rimosic (University of Alberta) as part of Quadratic forms\, linear algebr
aic groups and beyond\n\n\nAbstract\nFor $k$ a perfect field of characteri
stic $p > 0$ and $G$ a split reductive group over $k$ with $p$ a non-torsi
on prime for $G$\, we compute the mod $p$ motivic cohomology of the geomet
ric classifying space $BG_{(r)}$\, where $G_{(r)}$ is the $r$th Frobenius
kernel of $G$. Our main tool is a motivic version of the Eilenberg-Moore s
pectral sequence\, due to Krishna.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriya First (University of Haifa)
DTSTART;VALUE=DATE-TIME:20210120T163000Z
DTEND;VALUE=DATE-TIME:20210120T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/24
DESCRIPTION:Title: The Grothendieck--Serre conjecture for classical groups in low di
mensions\nby Uriya First (University of Haifa) as part of Quadratic fo
rms\, linear algebraic groups and beyond\n\n\nAbstract\nA famous conjectur
e of Grothendieck and Serre predicts that if $G$ is a reductive group sche
me over a semilocal regular domain $R$ and $X$ is a G-torsor\, then $X$ ha
s a point over the fraction field of $R$ if and only if it has an $R$-poin
t. I will discuss recent work with Eva Bayer-Fluckiger and Raman Parimala
in which we prove the conjecture for all forms of ${\\rm GL}_n$\, ${\\rm S
p}_n$ and ${\\rm SO}_n$ when $R$ is 2-dimensional\, and all forms of ${\\r
m GL}_{2n+1}$ when $R$ is 4-dimensional. (Here the ring $R$ is not require
d to contain a field.) We approach the problem using the hermitian Gersten
-Witt complex associated to an Azumaya algebra with involution $(A\,s)$ ov
er a semilocal regular ring $R$. Specifically\, we show that it is exact w
hen the Krull dimension of $R$ or the index of $A$ are sufficiently small.
\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kuznetsov (Steklov Mathematics Institute)
DTSTART;VALUE=DATE-TIME:20210127T163000Z
DTEND;VALUE=DATE-TIME:20210127T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/25
DESCRIPTION:Title: Exceptional collection of vector bundles on F4/P4\nby Alexand
er Kuznetsov (Steklov Mathematics Institute) as part of Quadratic forms\,
linear algebraic groups and beyond\n\n\nAbstract\nIn the talk I will expla
in a construction of a full exceptional collection of vector bundles on th
e homogeneous variety of the simple algebraic group of Dynkin type $F_4$ c
orresponding to its maximal parabolic subgroup $P_4$. The construction is
based on the relation of this homogeneous variety to a homogeneous variety
of type $E_6 / P_1$ and uses an exceptional collection constructed by Fae
nzi and Manivel. This is joint work with Pieter Belmans and Maxim Smirnov.
\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giancarlo Lucchini-Arteche (University of Chile)
DTSTART;VALUE=DATE-TIME:20210203T163000Z
DTEND;VALUE=DATE-TIME:20210203T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/26
DESCRIPTION:Title: Local-global principles for homogeneous spaces over some two-dime
nsional geometric global fields\nby Giancarlo Lucchini-Arteche (Univer
sity of Chile) as part of Quadratic forms\, linear algebraic groups and be
yond\n\n\nAbstract\nOver number fields\, there is a classic obstruction to
the local-global principle for the existence of rational points\, known a
s the Brauer-Manin obstruction\, which is conjectured to explain all failu
res of this principle for homogeneous spaces of connected linear groups. I
n the last few years\, there has been an increasing interest in fields of
a more geometric nature that are amenable to local-global principles and B
rauer-Manin obstructions as well. These include\, for instance\, function
fields of curves over discretely valued fields\, by analogy with the case
of global fields of positive characteristic. It is in this context that I
will present recent work with Diego Izquierdo on local-global principles f
or homogeneous spaces with connected stabilizers. We will see that\, altho
ugh some of the known results for number fields have direct analogs (that
can be obtained in the same way)\, the particularities of these new fields
bring up new counterexamples that cannot be explained by the Brauer-Manin
obstruction\, contrary to the number field case.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Panin (Steklov Institute at St.Petersburg)
DTSTART;VALUE=DATE-TIME:20210217T163000Z
DTEND;VALUE=DATE-TIME:20210217T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/27
DESCRIPTION:Title: Rationally isotropic quadratic spaces are locally isotropic (mixe
d characteristic case)\nby Ivan Panin (Steklov Institute at St.Petersb
urg) as part of Quadratic forms\, linear algebraic groups and beyond\n\n\n
Abstract\nA well-known conjecture of Colliot-Thélène asserts that a rati
onally isotropic quadratic space over a regular local ring is isotropic. I
f the ring contains a field\, then this conjecture was proved by the effor
ts of the speaker\, Pimenov and Scully. In the talk we will present new re
sults in the mixed characteristic case.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Brosnan (University of Maryland)
DTSTART;VALUE=DATE-TIME:20210210T163000Z
DTEND;VALUE=DATE-TIME:20210210T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/28
DESCRIPTION:Title: Fixed Points in Toroidal Compactifications and Essential Dimensio
n of Covers\nby Patrick Brosnan (University of Maryland) as part of Qu
adratic forms\, linear algebraic groups and beyond\n\n\nAbstract\nEssentia
l dimension is a numerical measure of the complexity of algebraic\nobjects
invented by J. Buhler and Z. Reichstein in the 90s. Roughly speaking\,\n
the essential dimension of an algebraic object is the number of parameters
it\ntakes to define the object over a field. For example\, by Kummer theo
ry\, it\ntakes one parameter to define a mu_n torsor\, so the essential di
mension of the\nfunctor of mu_n torsors (or the essential dimension of mu_
n for short) is 1.\nIn a preprint from 2019\, Farb\, Kisin and Wolfson (FK
W) prove theorems about the\nessential dimension of congruence covers of S
himura varieties using arithmetic\nmethods. In many cases\, they are able
to prove that the congruence covers are\nincompressible\, that is\, they
are not obtainable by base change from varieties\nof strictly smaller dime
nsion. \n\nIn my talk\, I will discuss recent work with Najmuddin Fakhrudd
in\, where we recover many (but definitely not all) of the results of FKW\
, by geometric\narguments using a new fixed point theorem. This also allow
s us to extend the\nincompressibility results of FKW to Shimura varieties
of exceptional type to\nwhich the arithmetic methods of FKW do not apply.
I will also discuss a general\nconjecture we make on the essential dimensi
on of congruence covers arising from\nHodge theory. (With some caveats\, w
e conjecture that it is equal to the\ndimension of the image of the period
map.)\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Hartmann (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20210224T163000Z
DTEND;VALUE=DATE-TIME:20210224T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/29
DESCRIPTION:Title: Local-global principles for constant reductive groups over arithm
etic function fields\nby Julia Hartmann (University of Pennsylvania) a
s part of Quadratic forms\, linear algebraic groups and beyond\n\n\nAbstra
ct\nArithmetic function fields are one variable function fields over compl
ete discretely valued fields. They naturally admit several collections of
overfields with respect to which one can study local-global principles. We
will focus on studying local-global principles for torsors under reductiv
e groups that are defined over the underlying discrete valuation ring\, re
porting on joint work with J.L.-Colliot-Thélène\, D. Harbater\, D. Krash
en\, R. Parimala\, and V. Suresh.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthieu Romagny (Université Rennes 1)
DTSTART;VALUE=DATE-TIME:20210317T153000Z
DTEND;VALUE=DATE-TIME:20210317T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/30
DESCRIPTION:Title: Smooth affine group schemes over the dual numbers\nby Matthie
u Romagny (Université Rennes 1) as part of Quadratic forms\, linear algeb
raic groups and beyond\n\n\nAbstract\nWe provide a geometric construction
for the equivalence between the category of smooth affine group schemes ov
er the ring of dual numbers $k[ε]$ and the category of extensions \\[ 1
→ {\\rm Lie}(G) → E → G → 1\, \\] where G is a smooth affine group
scheme over k. The equivalence is given by Weil restriction\, and we prov
ide a quasi-inverse which we call Weil extension. As an application\, we e
stablish a Dieudonné classification for smooth\, commutative\, unipotent
group schemes over $k[ε]$ when k is a perfect field.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Popov (Steklov Institute\, Moscow)
DTSTART;VALUE=DATE-TIME:20210310T163000Z
DTEND;VALUE=DATE-TIME:20210310T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/31
DESCRIPTION:Title: Root systems and root lattices in number fields\nby Vladimir
Popov (Steklov Institute\, Moscow) as part of Quadratic forms\, linear alg
ebraic groups and beyond\n\n\nAbstract\nThe following construction of a ro
ot system of type G_2 is given in J.-P. Serre’s book “Complex Semisimp
le Lie algebras” (Chapter V\, Section 16): “It can be described as the
set of algebraic integers of a cyclotomic field generated by a cubic root
of unity\, with norm 1 and 3”. The talk\, based on joint work with Yu.
G. Zarhin\, concerns the problem of realization of root systems\, their We
yl groups and their root lattices in the form of groups and lattices natur
ally associated with number fields.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Benoist (École normale supérieure\, Paris)
DTSTART;VALUE=DATE-TIME:20210303T163000Z
DTEND;VALUE=DATE-TIME:20210303T173000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/32
DESCRIPTION:Title: Sums of squares in local fields\nby Olivier Benoist (École n
ormale supérieure\, Paris) as part of Quadratic forms\, linear algebraic
groups and beyond\n\n\nAbstract\nArtin and Pfister have shown that a nonne
gative real\npolynomial in n variables is a sum of $2^n$ squares of ration
al functions. In other words\, the Pythagoras number of the field $\\mathb
b R(x_1\,…\,x_n)$ is at most $2^n$. In this talk\, I will consider local
variants of this statement. In particular\, I will give a proof of a conj
ecture of Choi\, Dai\, Lam and Reznick: the Pythagoras number of the field
of Laurent series $\\mathbb R((x_1\,…\,x_n))$ is at most $2^{n-1}$.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Brion (Institut Fourier\, Université Grenoble Alpes)
DTSTART;VALUE=DATE-TIME:20210324T153000Z
DTEND;VALUE=DATE-TIME:20210324T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/33
DESCRIPTION:Title: Homomorphisms of algebraic groups: representability and rigidity<
/a>\nby Michel Brion (Institut Fourier\, Université Grenoble Alpes) as pa
rt of Quadratic forms\, linear algebraic groups and beyond\n\n\nAbstract\n
The talk will address the following questions: given two algebraic groups
G\, H over a field\, is the functor of group homomorphisms from G to H rep
resentable by a scheme M\, locally of finite type? If so\, how to describe
the orbits of H acting on M via conjugation of homomorphisms? The represe
ntability question has a positive answer when G is reductive and H is smoo
th and affine\, by a result of Demazure in SGA3 (which holds over an arbit
ary base).The talk will present an extension of this result to the class o
f “semi-reductive” algebraic groups\, which includes reductive groups\
, finite groups and abelian varieties. In characteristic 0\, we will also
see that all the H-orbits in M are open. This rigidity property gives back
results of Vinberg and Margaux.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Lavrenov (St.Petersburg State University)
DTSTART;VALUE=DATE-TIME:20210331T153000Z
DTEND;VALUE=DATE-TIME:20210331T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/34
DESCRIPTION:Title: Morava motives of projective quadrics\nby Andrei Lavrenov (St
.Petersburg State University) as part of Quadratic forms\, linear algebrai
c groups and beyond\n\n\nAbstract\nThe category of Chow motives defined by
Grothendieck has plenty of various applications to quadratic forms\, and\
, more generally\, to projective homogeneous varieties. However\, there ar
e many open questions about the behaviour of Chow motives. In contrast\, i
f we change the Chow group by Grothendieck’s $K^0$ in the definition of
motives\, the resulting category behaves much more simply. One can define
the category of motives corresponding to any oriented cohomology theory A
and hopefully obtain invariants that are simpler than Chow motives but kee
p more information than $K^0$-motives.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly McKinnie (University of Montana)
DTSTART;VALUE=DATE-TIME:20210407T153000Z
DTEND;VALUE=DATE-TIME:20210407T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/35
DESCRIPTION:Title: Common Splitting Fields of Symbol Algebras\nby Kelly McKinnie
(University of Montana) as part of Quadratic forms\, linear algebraic gro
ups and beyond\n\n\nAbstract\nEvery central simple algebra of p-power degr
ee over a field of characteristic p is Brauer equivalent to a cyclic algeb
ra by a result of Albert. The proof of this and other similar p-algebra re
sults rely on the interplay between purely inseparable splitting fields an
d cyclic splitting fields of p-algebras. This talk on joint work with Adam
Chapman and Mathieu Florence looks at new results on common splitting fie
lds of symbol p-algebras with applications to symbol length.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Haution (LMU Munich)
DTSTART;VALUE=DATE-TIME:20210414T153000Z
DTEND;VALUE=DATE-TIME:20210414T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/36
DESCRIPTION:Title: The cobordism ring of algebraic involutions\nby Olivier Hauti
on (LMU Munich) as part of Quadratic forms\, linear algebraic groups and b
eyond\n\n\nAbstract\nI will provide an elementary definition of the cobord
ism ring of involutions of smooth projective varieties over a field (of ch
aracteristic not 2). I will describe its structure\, and give explicit “
stable” polynomial generators. I will draw some concrete consequences co
ncerning the geometry of fixed loci of involutions\, in terms of Chern num
bers. I will in particular mention an algebraic version of Boardman’s fi
ve halves theorem.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suresh Venapally (Emory University)
DTSTART;VALUE=DATE-TIME:20210505T153000Z
DTEND;VALUE=DATE-TIME:20210505T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/37
DESCRIPTION:Title: Degree three cohomology groups of function fields of curves over
number fields\nby Suresh Venapally (Emory University) as part of Quadr
atic forms\, linear algebraic groups and beyond\n\n\nAbstract\nLet $F$ be
a field and $l$ a prime not equal to the characteristic of $F$. Given $a_1
\, \\ldots \, a_n \\in F^∗$\, the cup product gives an element $(a_1)\\c
dot \\ldots \\cdot (a_n)$ in \n$H^n(F\, µ_l^{\\otimes n})$ and such an el
ement is called a symbol. Class field\ntheory asserts that if $F$ is a glo
bal field or a local field\, then every element in $H^2(F\, µ_l^{\\otimes
2})$ is a symbol. Let $F$ be the function field of a curve over a totally
imaginary number field or a local field. If $F$ contains a primitive $l$t
h root of unity\, then we show that every element in $H^3(F\, µ_l^{\\otim
es 3})$ is a symbol. We describe an\napplication to the isotropy of quadra
tic forms over F. We also give an application to the finite generation of
the Chow group of zero-cycles on quadric fibrations of curves over totally
imaginary number fields.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Guralnick (University of Southern California)
DTSTART;VALUE=DATE-TIME:20210512T153000Z
DTEND;VALUE=DATE-TIME:20210512T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/38
DESCRIPTION:Title: Generic Stabilizers for Simple Algebraic Groups\nby Robert Gu
ralnick (University of Southern California) as part of Quadratic forms\, l
inear algebraic groups and beyond\n\n\nAbstract\nConsider an algebraic gro
up $G$ acting on an irreducible variety $X$. We say there exists a gener
ic stabilizer for this action if there exists a nonempty open subset $Y$ o
f $X$ such that the stabilizers of any $y$ in $Y$ are all conjugate in $G$
. In characteristic $0$\, there are general results of Richardson proving
the existence of a generic stabilizer in many cases. We especially consi
der the case that $G$ is a simple algebraic group in positive characteris
tic and $X$ is an irreducible $G$-module. We show that a generic stabili
zer always exists and determine the generic stabilizer in all cases. This
fails for semisimple groups. This is joint work with Skip Garibaldi and R
oss Lawther.\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Zimmermann (Université d’Angers)
DTSTART;VALUE=DATE-TIME:20210519T153000Z
DTEND;VALUE=DATE-TIME:20210519T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/39
DESCRIPTION:by Susanna Zimmermann (Université d’Angers) as part of Quad
ratic forms\, linear algebraic groups and beyond\n\nInteractive livestream
: https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyNlV
EQT09\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/39/
URL:https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyN
lVEQT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Vishik (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20210526T153000Z
DTEND;VALUE=DATE-TIME:20210526T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/40
DESCRIPTION:by Alexander Vishik (University of Nottingham) as part of Quad
ratic forms\, linear algebraic groups and beyond\n\nInteractive livestream
: https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyNlV
EQT09\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/40/
URL:https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyN
lVEQT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Minac (University of Western Ontario)
DTSTART;VALUE=DATE-TIME:20210602T153000Z
DTEND;VALUE=DATE-TIME:20210602T163000Z
DTSTAMP;VALUE=DATE-TIME:20210514T193819Z
UID:Algebraicgroups/41
DESCRIPTION:by Jan Minac (University of Western Ontario) as part of Quadra
tic forms\, linear algebraic groups and beyond\n\nInteractive livestream:
https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyNlVEQ
T09\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Algebraicgroups/41/
URL:https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyN
lVEQT09
END:VEVENT
END:VCALENDAR