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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2016 Volume 443, Pages 46–60 (Mi znsl6256)

This article is cited in 2 papers

Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II

S. V. Vostokov, V. V. Volkov

St. Petersburg State University, St. Petersburg, Russia

Abstract: Current paper describes the explicit formula of the Hibert pairing between Milnor $K$-group of multidimensional local field and polynomial formal module. This formula generalizes similar results for one-dimensioinal case and multidimensional case of multiplicative group. A case of different characteristics of a field and its first residue field is considered.

Key words and phrases: formal groups, Hilbert symbol, mutidimensional local field, Milnor $K$-group.

UDC: 512.741

Received: 21.12.2015


 English version:
Journal of Mathematical Sciences (New York), 2017, 222:4, 394–403

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© Steklov Math. Inst. of RAS, 2025