A higher-dimensional Contou-Carrère symbol: local theory

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 -groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou...

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Bibliographic Details
Published inSbornik. Mathematics Vol. 206; no. 9; pp. 1191 - 1259
Main Authors Gorchinskiy, S. O., Osipov, D. V.
Format Journal Article
LanguageEnglish
Published London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.01.2015
Subjects
Boundaries
boundary map for $K$-groups
Construction
Contou-Carrère symbol
Formulas (mathematics)
Mathematical analysis
Symbols
Witt pairing
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Summary: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 -groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou-Carrère symbol over and we prove the integrality of this formula. We also study its relation with the higher-dimensional Witt pairing. Bibliography: 46 titles.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2015v206n09ABEH004494