Geodesic
A~higher-dimensional Contou-Carr\`ere symbol: local theory
Sbornik. Mathematics, Tome 206 (2015) no. 9, pp. 1191-1259

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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: boundary map for $K$-groups, Witt pairing.
Mots-clés : Contou-Carrère symbol 
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     author = {S. O. Gorchinskiy and D. V. Osipov},
     title = {A~higher-dimensional {Contou-Carr\`ere} symbol: local theory},
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S. O. Gorchinskiy; D. V. Osipov. A~higher-dimensional Contou-Carr\`ere symbol: local theory. Sbornik. Mathematics, Tome 206 (2015) no. 9, pp. 1191-1259. http://geodesic.mathdoc.fr/item/SM_2015_206_9_a1/