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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2005 Volume 321, Pages 183–196 (Mi znsl412)

Generalized Artin–Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field. II

A. N. Zinoviev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: In this paper we consider the generalized Hilbert symbol in a higher local field of charactersitic 0 with the first residue field of characteristic 0 as well and with perfect last residue field of positive characteristic p which comes from higher local $p$-class field theory developed by I. Fesenko. Using the descent to a subfield of mixed characteristic we deduce from the generalized Artin–Hasse and Iwasawa formulas proved in a previous paper the corresponding Artin–Hasse and Iwasawa explicit reciprocity laws in the case under consideration.

UDC: 512

Received: 23.12.2004


 English version:
Journal of Mathematical Sciences (New York), 2006, 136:3, 3935–3941

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© Steklov Math. Inst. of RAS, 2024