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 Contou-Carrère symbol over $\mathbb{Q}$ and we prove integrality of this formula. A relation with the higher-dimensional Witt pairing is also studied.

75 pages; minor changes

References in corpus (2)

• Tangent space to Milnor $K$-groups of rings
• Reciprocity laws and $K$-theory

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