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The two-dimensional Contou-Carrère symbol and reciprocity laws

Osipov, Denis and Zhu, Xinwen (2016) The two-dimensional Contou-Carrère symbol and reciprocity laws. Journal of Algebraic Geometry, 25 (4). pp. 703-774. ISSN 1534-7486. https://resolver.caltech.edu/CaltechAUTHORS:20140919-164513096

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Abstract

We define a two-dimensional Contou-Carrère symbol, which is a deformation of the two-dimensional tame symbol and is a natural generalization of the (usual) one-dimensional Contou-Carrère symbol. We give several constructions of this symbol and investigate its properties. Using higher categorical methods, we prove reciprocity laws on algebraic surfaces for this symbol. We also relate the two-dimensional Contou-Carrère symbol to the two-dimensional class field theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1305.6032arXivDiscussion Paper
https://doi.org/10.1090/jag/664 DOIArticle
http://www.ams.org/journals/jag/2016-25-04/S1056-3911-2016-00664-1/PublisherArticle
Additional Information:© Copyright 2016 University Press, Inc. Received by editor(s): July 28, 2013. Received by editor(s) in revised form: February 14, 2014, and May 6, 2014. Published electronically: April 22, 2016. D. O. partially supported by Russian Foundation for Basic Research (grants no. 14-01-00178-a, no. 13-01-12420 ofi_m2, and no. 12-01-33024 mol_a_ved) and by the Programme for the Support of Leading Scientific Schools of the Russian Federation (grant no. NSh-2998.2014.1). X. Z. partially supported by NSF grant DMS-1001280/1313894 and DMS-1303296 and by AMS Centennial Fellowship. The first author was supported by the Russian Foundation for Basic Research (grants No. 14-01-00178-a, No. 13-01-12420 ofi_m2, and No. 12-01-33024 mol_a_ved) and by the Programme for the Support of Leading Scientific Schools of the Russian Federation (grant No. NSh-2998.2014.1). The second author was partially supported by NSF grants DMS-1001280/1313894 and DMS-1303296 and by an AMS Centennial Fellowship.
Funders:
Funding AgencyGrant Number
Russian Foundation for Basic Research14-01-00178-a
Russian Foundation for Basic Research13-01-12420 ofi_m2
Russian Foundation for Basic Research12-01-33024 mol_a_ved
Programme for the Support of Leading Scientific Schools of the Russian FederationNSh-2998.2014.1
NSFDMS-1001280
NSFDMS-1313894
NSFDMS-1303296
AMS Centennial FellowshipUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20140919-164513096
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140919-164513096
Official Citation:The two-dimensional Contou-Carrère symbol and reciprocity laws Denis Osipov and Xinwen Zhu. J. Algebraic Geom. 25 (2016), 703-774
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49880
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Sep 2014 20:05
Last Modified:03 Oct 2019 07:18

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