Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Collection Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Organizer(s) Organising Committee: Aravind Asok (University of Southern California), Frédéric Déglise (CNRS Dijon), Grigory Garkusha (Swansea University), Paul Arne Østvær (University of Oslo) Scientific Committee: Eric M. Friedlander (University of Southern California), Haynes R. Miller (MIT Department of Mathematics), Bertrand Toën (CNRS Toulouse)
Date(s) 06/07/2020 - 17/07/2020
linked URL https://indico.math.cnrs.fr/event/5160/
00:00:00 / 00:00:00
7 28

Pullbacks for the Rost-Schmid Complex

By Tom Bachmann

Notes: https://nextcloud.ihes.fr/index.php/s/9AE3otsf8XJ6M8a Let ? be a perfect field and ? a strictly homotopy invariant sheaf of abelian groups on Sm_?. The cousin complex can be used to compute the cohomology of a smooth variety ? over ? with coefficients in ?. However, if ? → ? is a morphism of smooth varieties, there is not in general an induced map on cousin complexes, so computing pullbacks of cohomology classes is difficult. In this talk I will explain how such pullbacks may nonetheless be computed, at least up to choosing a good enough cycle representing the cohomology class (which is always possible in principle, but may be difficult in practice). Time permitting, I will mention applications to the ?_?-stabilization conjecture (which was formulated jointly with Maria Yakerson).

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