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Nondiscrete local ramified class field theory. (English) Zbl 0874.11076

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 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 I. Fesenko and S. Vostokov, “Local fields and their extensions” [Translations of Mathematical Monographs 121 (1993; Zbl 0781.11042)].

MSC:

11S31 Class field theory; \(p\)-adic formal groups
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