The two-dimensional Contou-Carrère symbol and reciprocity laws

Osipov, Denis; Zhu, Xinwen

doi:10.1090/jag/664

Authors: Denis Osipov and Xinwen Zhu
Journal: J. Algebraic Geom. 25 (2016), 703-774
DOI: https://doi.org/10.1090/jag/664
Published electronically: April 22, 2016
MathSciNet review: 3533184
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Abstract | References | Additional Information

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.

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Additional Information

Denis Osipov
Affiliation: Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia – and – National University of Science and Technology MISIS, Leninskii pr. 4, Moscow, 119049 Russia
Email: d_osipov@mi.ras.ru

Xinwen Zhu
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Address at time of publication: Department of Mathematics, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125
MR Author ID: 868127
Email: xzhu@caltech.edu

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
Additional Notes: 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
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