Tame Galois \(p\)-extensions of \(p\)-Henselian fields
type: Item
instance of: scholarly article
title: Tame Galois \(p\)-extensions of \(p\)-Henselian fields
zbMATH Open document ID: 1005.12001
author: Antonio Engler
author: Alexander Prestel
published in: Manuscripta Mathematica
publication date: 2003-02-25T00:00:00Z
review text: A valued field \(K\) is called \(p\)-Henselian if its valuation extends uniquely to the maximal Galois \(p\)-extension \(K(p)\) of \(K\). The main theorem of the paper under review gives a determination of the structure of the Galois group \(G_K(p)\) of the extension \(K(p)/K\) in case the characteristic of the residue field \(\overline{K}\) is different from \(p\). We get \[ G_K(p)\simeq T\rtimes G_{\overline{K}} (p), \] where \(T\) is the inertia group of \(G_K(p)\). Further \(T\simeq \mathbb{Z}_p^\mu\) for some \(\mu\). The operation of \(G_{\overline{K}}(p)\) on \(\mathbb{Z}_p^\mu\) is given by the \(p\)-cyclotomic characters. The possible values of \(\mu\) are described.
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12J10
zbMATH DE Number: 1334554
zbMATH Keywords: Henselian fields
zbMATH Keywords: Galois groups
zbMATH Keywords: maximal Galois \(p\)-extension
zbMATH Keywords: \(p\)-cyclotomic characters
reviewed by: Martin Epkenhans
MaRDI profile type: Publication
full work available at URL: s002290050172
OpenAlex ID: W2043732206
DOI: 10.1007/S002290050172
description: scientific article; zbMATH DE number 1334554