CNRS Poncelet

Conference "Global Fields"

October 25 - 28, 2011

Moscow, Russia

 RAS Poncelet

Organisers: Philippe Lebacque (Laboratoire de Mathématiques de Besançon ), Michael Tsfasman (CNRS, Laboratoire Poncelet, Institute for Information Transmission Problems), Alexey Zykin (Laboratoire Poncelet, State University Higher School of Economics, IITP)

Two-dimensional Contou-Carrere symbol, reciprocity laws and higher class field theory

Denis Osipov (Moscow)

Thursday 27 October, 12:30 - 14:00

Abstract

I will define the tri-multiplicative anti-symmetric map from the triple product of the double loop group of multiplicative group over integers to the multiplicative group. This map is called the two-dimensional Contou-Carrere symbol. I will explain the first properties of this symbol. I will prove the reciprocity laws for this symbol on algebraic surfaces over finite fields. I will explain how all reciprocity laws which one needs to construct Parshin-Kato global two-dimensional class field theory can be obtained from reciprocity laws for two-dimensional Contou-Carrere symbol.

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