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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Victor Abrashkin

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

Author(s) from Durham

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.