The two-dimensional Contou-Carr\`ere symbol and reciprocity laws
Abstract
We define a two-dimensional Contou-Carr\`ere symbol, which is a deformation of the two-dimensional tame symbol and is a natural generalization of the (usual) one-dimensional Contou-Carr\`ere 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\`ere symbol with the two-dimensional class field theory.
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