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Groups of automorphisms of local fields of period p^M and nilpotent class < p

Abrashkin, Victor

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Abstract

Suppose K is a finite field extension of Qp containing a pM-th primitive root of unity. For 1 6 s < p denote by K[s, M] the maximal p-extension of K with the Galois group of period pM and nilpotent class s. We apply the nilpotent Artin–Schreier theory together with the theory of the field-of-norms functor to give an explicit description of the Galois groups of K[s, M]/K. As application we prove that the ramification subgroup of the absolute Galois group of K with the upper index v acts trivially on K[s, M] iff v > eK(M + s/(p − 1)) − (1 − δ1s)/p, where eK is the ramification index of K and δ1s is the Kronecker symbol.

Journal Article Type Article
Acceptance Date Jun 14, 2016
Online Publication Date Sep 22, 2016
Publication Date Jun 1, 2017
Deposit Date Sep 13, 2016
Publicly Available Date Oct 14, 2016
Journal Annales de l'Institut Fourier
Print ISSN 0373-0956
Electronic ISSN 1777-5310
Publisher Association des Annales de l'Institut Fourier
Peer Reviewed Peer Reviewed
Volume 67
Issue 2
Pages 605-635
DOI https://doi.org/10.5802/aif.3093
Public URL https://durham-repository.worktribe.com/output/1375069

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