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arXiv · 1305.6032

The two-dimensional Contou-Carr\`{e}re symbol and reciprocity laws

Denis Osipov·Xinwen Zhu
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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.

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Denis Osipov, Xinwen Zhu. 2013-05-26. The two-dimensional Contou-Carr\`{e}re symbol and reciprocity laws. https://doi.org/10.1090/jag/664

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