On the structure of certain Galois cohomology groups

Abstract

This paper primarily concerns Galois cohomology groups associated to Galois representations over a complete local ring $R$. The underlying Galois module and the corresponding cohomology groups which we consider are discrete $R$-modules. Under certain hypotheses, we prove that the first cohomology group is an almost divisible $R$-module. We also consider the subgroup of locally trivial elements in the second cohomology group, proving under certain hypotheses that it is a coreflexive $R$-module.