Published 2011
| Published + Accepted Version
Journal Article
Open
A categorical proof of the Parshin reciprocity laws on algebraic surfaces
- Creators
- Osipov, Denis
- Zhu, Xinwen
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 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.
Additional Information
© 2011 Mathematical Sciences Publishers. Received: 27 February 2010. Revised: 25 October 2010. Accepted: 21 November 2010. Published: 10 September 2010. Osipov was financially supported by Russian Foundation for Basic Research (grant no. 11-01-00145) and by the Programme for the Support of Leading Scientific Schools of the Russian Federation (grant no. NSh-4713.2010.1). Zhu's research is supported by NSF grant under DMS-1001280. Osipov is grateful to L. Breen, M. Kapranov and A. N. Parshin for useful discussions on categorical approach to the two-dimensional tame symbol at various periods of time. Zhu thanks V. Kac for useful discussions.Attached Files
Published - ant-v5-n3-p01-p.pdf
Accepted Version - 1002.4848v3.pdf
Files
1002.4848v3.pdf
Files
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Additional details
- Eprint ID
- 49871
- Resolver ID
- CaltechAUTHORS:20140919-152325174
- 11-01-00145
- Russian Foundation for Basic Research
- NSh-4713.2010.1
- Programme for the Support of Leading Scientific Schools of the Russian Federation
- DMS-1001280
- NSF
- Created
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2014-09-23Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field