On The Structure of Certain Galois Cohomology Groups

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.

2000 Mathematics Subject Classification: 11R23, 11R34

Keywords and Phrases: Galois cohomology, Iwasawa theory

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