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arXiv · 1002.4848

A categorical proof of the Parshin reciprocity laws on algebraic surfaces

Denis Osipov·Xinwen Zhu
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Abstract

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 it in the context of two-dimensional local fields and two-dimensional adelic theory we obtain the two-dimensional tame symbol and a new proof of Parshin reciprocity laws on an algebraic surface.

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BibTeXRIS

Denis Osipov, Xinwen Zhu. 2010-11-22. A categorical proof of the Parshin reciprocity laws on algebraic surfaces. https://doi.org/10.2140/ant.2011.5.289

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