Vol. 5, No. 3, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 7, 1559–1821
Issue 6, 1311–1557
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
A categorical proof of the Parshin reciprocity laws on algebraic surfaces

Denis Osipov and Xinwen Zhu

Vol. 5 (2011), No. 3, 289–337
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.

Keywords
Picard groupoids, central extensions, commutator maps, two-dimensional local fields, higher adeles, reciprocity laws
Mathematical Subject Classification 2000
Primary: 19F15
Secondary: 18D05
Milestones
Received: 27 February 2010
Revised: 25 October 2010
Accepted: 21 November 2010
Published: 10 September 2011
Authors
Denis Osipov
Steklov Mathematical Institute
Gubkina str. 8
Moscow
119991
Russia
Xinwen Zhu
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA, 02138
United States