Value groups of Henselian valuations
type: Item
instance of: scholarly article
title: Value groups of Henselian valuations
zbMATH Open document ID: 0804.12005
author: Tsuneo Kanno
author: Takeo Shirasou
published in: Proceedings of the Japan Academy. Series A
publication date: 1995-01-23T00:00:00Z
review text: A system \((G, A,\deg, v)\) is called admissible situation over \(k\), if \(G\) is a pro-finite group with \((G_ K)\) closed subgroups of \(G\) indexed by fields \(K\), \(G= G_ k\), \(A\) is a multiplicative \(G\)-module, \(\deg: G\to \widehat {\mathbb{Z}}\) a surjective continuous homomorphism and \(v_ K: A_ K\to \widehat {\mathbb{Z}}\) is a Henselian valuation with respect to deg, where \(A_ K\) is the submodule of \(A\) of elements fixed by \(G_ K\). The authors then prove that if \((G,A, \deg,v)\) and \((G,A, \deg,v')\) are admissible situations such that the class field axiom holds for any subextension \(L/K\) of \(K\widetilde{k}/K\) in both situations (where \(\widetilde{k}\) is such that \(G_{\widetilde{k}}\) is the kernel of deg), the valuations \(v_ K\) and \(v'_ K\) have the same unit group.
Mathematics Subject Classification ID: 12J10
zbMATH DE Number: 549029
zbMATH Keywords: Henselian valuation
reviewed by: Jiří Močkoř
MaRDI profile type: Publication
full work available at URL: pjaa.69.268
OpenAlex ID: W2043096268
cites work: Neubegründung der Klassenkörpertheorie
cites work: Q3714149
DOI: 10.3792/PJAA.69.268
description: scientific article; zbMATH DE number 549029