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Local class field theory. (English. Russian original) Zbl 1080.11082
St. Petersbg. Math. J. 15, No. 6, 837-846 (2004); translation from Algebra Anal. 15, No. 6, 35-47 (2003).
The author gives condition for a Henselian field \(F\) which imply that local class field theory is valid for \(F\) in the sense that for every finite Galois extension \(F_0\) of \(F\) the reciprocity map \(\text{Gal}(F_0/F) \to F^{\times}/N_{F_0/F}(F_0^{\times})\) induces an isomorphism of the projection to \(\text{Gal}(F_0/F)^{ab}\). He gives an example of a field \(F\) which shows that these conditions are less restrictive than the applicability of J. Neukirch’s abstract class field theory [Algebraic number theory. Transl. from the German by Norbert Schappacher. Grundlehren der Mathematischen Wissenschaften. 322 (Berlin: Springer) (1999; Zbl 0956.11021), Chapter IV].

11S31 Class field theory; \(p\)-adic formal groups
Full Text: DOI
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