English

A higher-dimensional Contou-Carr\`ere symbol: local theory

Algebraic Geometry 2016-03-03 v3 K-Theory and Homology Number Theory

Abstract

We construct a higher-dimensional Contou-Carr\`ere symbol and we study its various fundamental properties. The higher-dimensional Contou-Carr\`ere symbol is defined by means of the boundary map for KK-groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou-Carr\`ere symbol over Q\mathbb Q and we prove integrality of this formula. A relation with the higher-dimensional Witt pairing is also studied.

Cite

@article{arxiv.1505.03829,
  title  = {A higher-dimensional Contou-Carr\`ere symbol: local theory},
  author = {Sergey Gorchinskiy and Denis Osipov},
  journal= {arXiv preprint arXiv:1505.03829},
  year   = {2016}
}

Comments

75 pages; minor changes

R2 v1 2026-06-22T09:34:27.375Z