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

Abrashkin, Victor

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.

Citation

Abrashkin, V. (2017). Groups of automorphisms of local fields of period p^M and nilpotent class < p. Annales de l'Institut Fourier, 67(2), 605-635. https://doi.org/10.5802/aif.3093

• 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