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SUMMARY:Tom Bachmann (LMU Munich)
DTSTART:20200415T080000Z
DTEND:20200415T091500Z
DTSTAMP:20260416T075251Z
UID:MoVid-20/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoVid-20/1/"
 >Pullbacks for the Rost-Schmid complex</a>\nby Tom Bachmann (LMU Munich) a
 s part of MoVid-20\n\n\nAbstract\nLet $F$ be a "strictly homotopy invarian
 t" Nisnevich sheaf of abelian groups on the site of smooth varieties over 
 a perfect field $k$. By work of Morel and Colliot-Thélène--Hoobler--Kahn
 \, the cohomology of $F$ may be computed using a fairly explicit "Rost-Sch
 mid" complex. However\, given a morphism $f: X \\to Y$ of smooth varieties
 \, it is in general (in particular if f is not flat\, e.g. a closed immers
 ion) unclear how to compute the pullback map $f^*: H^*(Y\, F) \\to H^*(X\,
 F)$ in terms of the Rost-Schmid complex. I will explain how to compute the
  pullback of a cycle with support $Z$ such that $f^{-1}(Z)$ has the expect
 ed dimension. Time permitting\, I will sketch how this implies the followi
 ng consequence\, obtained in joint work with Maria Yakerson: given a point
 ed motivic space $X$\, its zeroth $P^1$-stable homotopy sheaf is given by 
 $\\pi_3(\\Sigma^3_{P^1} X)_{-3}$.\n
LOCATION:https://researchseminars.org/talk/MoVid-20/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Hoyois (Universität Regensburg)
DTSTART:20200415T100000Z
DTEND:20200415T111500Z
DTSTAMP:20260416T075251Z
UID:MoVid-20/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoVid-20/2/"
 >Milnor excision for motivic spectra</a>\nby Marc Hoyois (Universität Reg
 ensburg) as part of MoVid-20\n\n\nAbstract\nIt is a classical result of We
 ibel that homotopy invariant algebraic K-theory satisfies excision\, in th
 e sense that for any ring $A$ and ideal $I\\subset A$\, the fiber of $KH(A
 ) \\to KH(A/I)$ depends only on $I$ as a nonunital ring. In joint work wit
 h Elden Elmanto\, Ryomei Iwasa\, and Shane Kelly\, we show that this is tr
 ue more generally for any cohomology theory represented by a motivic spect
 rum.\n
LOCATION:https://researchseminars.org/talk/MoVid-20/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Yakerson (Universität Regensburg)
DTSTART:20200415T123000Z
DTEND:20200415T134500Z
DTSTAMP:20260416T075251Z
UID:MoVid-20/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoVid-20/3/"
 >Motivic generalized cohomology theories from framed perspective</a>\nby M
 aria Yakerson (Universität Regensburg) as part of MoVid-20\n\n\nAbstract\
 nAll motivic generalized cohomology theories acquire unique structure of s
 o called framed transfers. If one takes framed transfers into account\, it
  turns out that many interesting cohomology theories can be constructed si
 mply as suspension spectra on certain moduli stacks (and their variations)
 . This way important cohomology theories on schemes get new geometric inte
 rpretations\, and so do  canonical maps between different cohomology theor
 ies. In the talk we will explain the general formalism of framed transfers
  and show how it works for various cohomology theories. This is a summary 
 of joint projects with Tom Bachmann\, Elden Elmanto\, Marc Hoyois\, Joachi
 m Jelisiejew\, Adeel Khan\, Denis Nardin and Vladimir Sosnilo.\n
LOCATION:https://researchseminars.org/talk/MoVid-20/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Nardin (Universität Regensburg)
DTSTART:20200415T143000Z
DTEND:20200415T154500Z
DTSTAMP:20260416T075251Z
UID:MoVid-20/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoVid-20/4/"
 >A description of the motive of $\\mathrm{Hilb}(\\mathbb{A}^\\infty)$</a>\
 nby Denis Nardin (Universität Regensburg) as part of MoVid-20\n\n\nAbstra
 ct\nThe Hilbert scheme of points in infinite affine space is a very compli
 cated algebro-geometric object\, whose local structure is extremely rich a
 nd hard to describe. In this talk I will show that nevertheless its motive
  is pure Tate and in fact it coincides with the motive of the Grassmannian
 . This will allow us to give a simple conceptual description of the motivi
 c algebraic K-theory spectrum. This is joint work with Marc Hoyois\, Joach
 im Jelisiejew\, Burt Totaro and Maria Yakerson.\n
LOCATION:https://researchseminars.org/talk/MoVid-20/4/
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