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

Abrashkin, Victor (2017) 'Groups of automorphisms of local fields of period p^M and nilpotent class < p.', Annales de l'Institut Fourier., 67 (2). pp. 605-635.

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.

Item Type:Article
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Available under License - Creative Commons Attribution No Derivatives.
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Status:Peer-reviewed
Publisher Web site:http://aif.cedram.org/item?id=AIF_2017__67_2_605_0
Publisher statement:Cet article est mis à disposition selon les termes de la licence CREATIVE COMMONS ATTRIBUTION – PAS DE MODIFICATION 3.0 FRANCE. http://creativecommons.org/licenses/by-nd/3.0/fr/
Date accepted:14 June 2016
Date deposited:14 October 2016
Date of first online publication:22 September 2016
Date first made open access:No date available

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