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).