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JOURNALS // Matematicheskii Sbornik // Archive
Mat. Sb., 2013 Volume 204, Number 6, Pages 3–22 (Mi sm8205)
This article is cited in 3 papers

Shafarevich's paper “A general reciprocity law”

S. V. Vostokov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: A new method for calculating an explicit form of the Hilbert pairing is proposed. It is used to calculate the Hilbert pairing in a classical local field and in a complete higher-dimensional field.
Bibliography: 25 titles.

Keywords: explicit reciprocity laws, complete higher-dimensional fields, topological $K$-groups.

UDC: 517.538

MSC: Primary 11S70; Secondary 11S15, 19D45

Received: 25.12.2012

DOI: 10.4213/sm8205


 English version: Sbornik: Mathematics, 2013, 204:6, 781–800

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© Steklov Math. Inst. of RAS, 2025