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arXiv · math/0505543

Demuskin groups, Galois modules, and the elementary type conjecture

John Labute·Nicole Lemire·Jan Minac·John Swallow
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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).

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John Labute, Nicole Lemire, Jan Minac, John Swallow. 2005-12-24. Demuskin groups, Galois modules, and the elementary type conjecture. https://doi.org/10.1016/j.jalgebra.2005.12.021

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