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SUMMARY:Tom Bachmann (LMU Munich)
DTSTART:20200415T080000Z
DTEND:20200415T091500Z
DTSTAMP:20260418T105735Z
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/
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