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# A categorical proof of the Parshin reciprocity laws on algebraic surfaces

@inproceedings{Osipov2011ACP, title={A categorical proof of the Parshin reciprocity laws on algebraic surfaces}, author={Denis Osipov and X Zhu}, year={2011} }

- Published 2011
DOI:10.2140/ant.2011.5.289

We define and study the 2-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.