This article is cited in 17 papers

A higher-dimensional Contou-Carrère symbol: local theory

S. O. Gorchinskiy, D. V. Osipov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We construct a higher-dimensional Contou-Carrère symbol and we study some of its fundamental properties. The higher-dimensional Contou-Carrère symbol is defined by means of the boundary map for $K$-groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou-Carrère symbol over $\mathbb Q$ and we prove the integrality of this formula. We also study its relation with the higher-dimensional Witt pairing.
Bibliography: 46 titles.

Keywords: Contou-Carrère symbol, boundary map for $K$-groups, Witt pairing.

UDC: 512.71+512.666+511.687

MSC: Primary 19D45; Secondary 19F15

Received: 25.03.2015

DOI: 10.4213/sm8516

 English version: Sbornik: Mathematics, 2015, 206:9, 1191–1259

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ArXiv: 1505.03829