Demuskin groups, Galois modules, and the elementary type conjecture
arXiv:math/0505543 · doi:10.1016/j.jalgebra.2005.12.021
Abstract
Let p be a prime and F(p) the maximal p-extension of a field F containing a primitive p-th root of unity. We give a new characterization of Demuskin groups among Galois groups Gal(F(p)/F) when p=2, and, assuming the Elementary Type Conjecture, when p>2 as well. This characterization is in terms of the structure, as Galois modules, of the Galois cohomology of index p subgroups of Gal(F(p)/F).
v2 (20 pages); added theorem characterizing decompositions into free and trivial modules; to appear in J. Algebra