A Note on Galois Cohomology of Algebraic Integers

Abstract

We consider an admissible system ({\\mathfrak g},(G,M)) where {\\mathfrak g} is the group of a Galois extension k⁄Q of number fields, G the ring {\\mathcal O}_k of integers of k and M=({\\mathcal O}_k)². The cohomology group H¹({\\mathfrak g},{\\mathcal O}_k) is nicely described by a naive submodule Ξ_k of {\\mathcal O}_k and the Poincaré index i_γ({\\mathfrak g},M), γ∈H¹({\\mathfrak g},{\\mathcal O}_k), for the system ({\\mathfrak g},(G,M)), can be expressed in terms of Ξ_k.