Conference "Zeta Functions"

Noncommutative reciprocity laws and non-ramified Langlands correspondence on two-dimensional arithmetic schemes

Denis Osipov (Moscow)

Thursday, November 22, 11:45 - 12:45

Video: [mp4]

Abstract

Following an approach of M. Kapranov we will describe an idea what should be a two-dimensional generalization of the Langlands correpondence. The local object on a two-dimensional scheme is a two-dimensional local field. We will describe an analog of principal series representations for general linear groups over two-dimensional local fields. The main ingredient of this construction is some central extension of this group. We will prove the reciprocity laws for these central extensions, i.e. the splittings of these central extensions over some subgroups which are connected either with points or with  integral one-dimenisonal subschemes of a given two-dimensional arithemetic scheme (i.e. of an algebraic surface over a finite field or of an arithmetic surface).