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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Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution No Derivatives. Download PDF (Advance online version) (736Kb) |
Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution No Derivatives. Download PDF (Final published version) (738Kb) |
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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