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Article

The two-dimensional Contou-Carrere symbol and reciprocity laws

Journal of Algebraic Geometry. 2016. Vol. 25. P. 703-774.
Osipov D., Zhu X.

We define a two-dimensional Contou-Carrere symbol, which is a deformation of the two-dimensional tame symbol and is a natural generalization of the usual (one-dimensional) Contou-Carrere 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 also relate the two-dimensional Contou-Carrere symbol with the two-dimensional class field theory.