Nondiscrete local ramified class field theory
type: Item
instance of: scholarly article
title: Nondiscrete local ramified class field theory
zbMATH Open document ID: 0874.11076
author: Adrian Iovita
author: Alexandru Zaharescu
published in: Journal of Mathematics of Kyoto University
publication date: 1997-11-11T00:00:00Z
review text: The paper actually contains abelian class field theory of a field \(k\) which is an infinite algebraic extension of \(\mathbb{Q}_p\) with finite residue degree and finite exponent of \(p\) in the Steinitz number of the degree \(|k:Q_p|\). As a generalization of classical local class field theory the results of the paper have been known for at least 40 years; for instance, see Section 2 of \textit{Y. Kawada's} paper [Duke Math. J. 22, 165-177 (1955; Zbl 0067.01904)]. Looking at more recent literature, the main theorem 6.1 of the paper follows easily from Exercise 6, Section 1, Chapter V of the book by \textit{I. Fesenko} and \textit{S. Vostokov}, ``Local fields and their extensions'' [Translations of Mathematical Monographs 121 (1993; Zbl 0781.11042)].
Mathematics Subject Classification ID: 11S31
zbMATH DE Number: 836416
zbMATH Keywords: local class field theory
zbMATH Keywords: abelian class field theory
zbMATH Keywords: Steinitz number
reviewed by: I. B. Fesenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518774
OpenAlex ID: W1523075548
DOI: 10.1215/KJM/1250518774
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description: scientific article; zbMATH DE number 836416