  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.
