Nondiscrete local ramified class field theory
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)].
scientific article; zbMATH DE number 836416
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