The two-dimensional Contou-Carr\`{e}re symbol and reciprocity laws
Algebraic Geometry
2016-07-29 v2 Category Theory
Number Theory
Abstract
We define a two-dimensional Contou-Carr\`{e}re symbol, which is a deformation of the two-dimensional tame symbol and is a natural generalization of the (usual) one-dimensional Contou-Carr\`{e}re symbol. We give several constructions of this symbol and investigate its properties. Using higher categorical methods, we prove reciprocity laws on algebraic surfaces for this symbol. We relate also the two-dimensional Contou-Carr\`{e}re symbol with the two-dimensional class field theory.
Keywords
Cite
@article{arxiv.1305.6032,
title = {The two-dimensional Contou-Carr\`{e}re symbol and reciprocity laws},
author = {Denis Osipov and Xinwen Zhu},
journal= {arXiv preprint arXiv:1305.6032},
year = {2016}
}
Comments
58 pages; revised version: added K-theory approach; to appear in Journal of Algebraic Geometry