Abstract
We define and study the -category of torsors over a Picard groupoid, a central extension of a group by a Picard groupoid, and commutator maps in this central extension. Using this in the context of two-dimensional local fields and two-dimensional adèle theory we obtain the two-dimensional tame symbol and a new proof of Parshin reciprocity laws on an algebraic surface.
Citation
Denis Osipov. Xinwen Zhu. "A categorical proof of the Parshin reciprocity laws on algebraic surfaces." Algebra Number Theory 5 (3) 289 - 337, 2011. https://doi.org/10.2140/ant.2011.5.289
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