Demuskin groups, Galois modules, and the elementary type conjecture
数论
2007-05-23 v2
摘要
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).
引用
@article{arxiv.math/0505543,
title = {Demuskin groups, Galois modules, and the elementary type conjecture},
author = {John Labute and Nicole Lemire and Jan Minac and John Swallow},
journal= {arXiv preprint arXiv:math/0505543},
year = {2007}
}
备注
v2 (20 pages); added theorem characterizing decompositions into free and trivial modules; to appear in J. Algebra