2015
DOI: 10.1070/sm2015v206n09abeh004494
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A higher-dimensional Contou-Carrère symbol: local theory

Abstract: We construct a higher-dimensional Contou-Carrère symbol and we study its various 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 ContouCarrère symbol over Q and we prove integrality of this formula. A relation with the higher-dimensional Witt pairing is also studied.

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Cited by 17 publications
(41 citation statements)
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“…The results of this paper will be applied in a forthcoming paper [9] to further investigations of the n-dimensional Contou-Carrère symbol, which was studied by Contou-Carrère himself in [1,2] for the case n = 1, by the second named author and Zhu in [14] for the case n = 2, and by the authors in [6,7,8] for arbitrary n.…”
Section: Introductionmentioning
confidence: 92%
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“…The results of this paper will be applied in a forthcoming paper [9] to further investigations of the n-dimensional Contou-Carrère symbol, which was studied by Contou-Carrère himself in [1,2] for the case n = 1, by the second named author and Zhu in [14] for the case n = 2, and by the authors in [6,7,8] for arbitrary n.…”
Section: Introductionmentioning
confidence: 92%
“…In this section, we introduce notation and recall, mainly from [8], facts on the ring of iterated Laurent series, the topology on this ring, the group of its invertible elements, its differential forms, and on the higher-dimensional residue map.…”
Section: Preliminaries and Notationmentioning
confidence: 99%
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