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Sbornik: Mathematics, 2015, Volume 206, Issue 9, Pages 1191–1259
DOI: https://doi.org/10.1070/SM2015v206n09ABEH004494 (Mi sm8516) 		 
This article is cited in 16 scientific papers (total in 16 papers)

A higher-dimensional Contou-Carrère symbol: local theory

S. O. Gorchinskiy, D. V. Osipov

Steklov Mathematical Institute of Russian Academy of Sciences
English version PDF (997 kB) Citations (16) Russian version article
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DOI: https://doi.org/10.1070/SM2015v206n09ABEH004494
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.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.
Received: 25.03.2015
Bibliographic databases:
Document Type: Article
UDC: 512.71+512.666+511.687
MSC: Primary 19D45; Secondary 19F15
Language: English
Original paper language: Russian
Citation: S. O. Gorchinskiy, D. V. Osipov, “A higher-dimensional Contou-Carrère symbol: local theory”, Sb. Math., 206:9 (2015), 1191–1259
Citation in format AMSBIB
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\paper A~higher-dimensional Contou-Carr\`ere symbol: local theory
\jour Sb. Math.
\yr 2015
\vol 206
\issue 9
\pages 1191--1259
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