Demuskin groups, Galois modules, and the elementary type conjecture

Details Demuskin groups, Galois modules, and the elementary type conjecture Demuskin groups, Galois modules, and the elementary type conjecture

2005-05-25

arxiv.org/abs/math/0505543v2

J. Algebra 304 (2006), no. 2, 1130--1146

Mathematics

Number Theory

v2 (20 pages); added theorem characterizing decompositions into free and trivial modules; to appear in J. Algebra

Scientific paper

10.1016/j.jalgebra.2005.12.021

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).

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