Tom Bachmann - Pullbacks for the Rost-Schmid Complex
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2020-07-28

Notes: https://nextcloud.ihes.fr/index.php/s/9AE3otsf8XJ6M8a

Let 𝑘 be a perfect field and 𝑀 a strictly homotopy invariant sheaf of abelian groups on Sm_𝑘. The cousin complex can be used to compute the cohomology of a smooth variety 𝑋 over 𝑘 with coefficients in 𝑀. However, if 𝑋 → 𝑌 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 𝔾_𝑚-stabilization conjecture (which was formulated jointly with Maria Yakerson).