Groups of automorphisms of local fields of period p and nilpotent class

Groups of automorphisms of local fields of period p and nilpotent class < p, II

Published:2017-09 Issue:10 Volume:28 Page:1750066
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Abrashkin Victor¹²

Affiliation:

1. Department of Mathematical Sciences, Durham University, Science Laboratories, South Rd, Durham DH1 3LE, UK

2. Steklov Institute, Gubkina str. 8, 119991, Moscow, Russia

Abstract

Suppose [Formula: see text] is a finite field extension of [Formula: see text] containing a primitive [Formula: see text]th root of unity. Let [Formula: see text] be the maximal quotient of period [Formula: see text] and nilpotent class [Formula: see text] of the Galois group of a maximal [Formula: see text]-extension of [Formula: see text]. We describe the ramification filtration [Formula: see text] and relate it to an explicit form of the Demushkin relation for [Formula: see text]. The results are given in terms of Lie algebras attached to the appropriate [Formula: see text]-groups by the classical equivalence of the categories of [Formula: see text]-groups and Lie algebras of nilpotent class [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X17500665

Reference11 articles.

1. Galois groups of local fields, Lie algebras and ramification

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

3. Groups of automorphisms of local fields of period p and nilpotent class < p, I

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