On the cohomology of tori over local fields with perfect residue field

Alessandra Bertapelle, Cristian D. Gonzalez-Aviles

Published 2013-11-19, updated 2013-12-03Version 3

If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension <= 1, our results have a particularly simple form and yield, more generally, isomorphisms between the abelian K-cohomology of a reductive group G over K and the k-cohomology of a certain quotient of the algebraic fundamental group of G.