Galois module structure of local unit groups

Details Galois module structure of local unit groups Galois module structure of local unit groups

2011-08-16

arxiv.org/abs/1108.3328v2

Mathematics

Number Theory

37 pages; to appear in Algebra & Number Theory

Scientific paper

We study the groups in the unit filtration of a finite abelian extension K of the field of p-adic numbers. We determine explicit generators of these groups as modules over the pro-p group ring of the Galois group of K over the p-adic numbers. We work in eigenspaces for powers of the Teichmueller character, first at the level of the field of norms for the extension of K by p-power roots of unity and then at the level of K.

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