Unramified two-dimensional Langlands correspondence

Abstract

In this paper we describe the unramified Langlands correspondence for two-dimensional local fields, we construct a categorical analogue of the unramified principal series representations and study its properties. The main tool for this description is the construction of a central extension. For this (and other) central extension we prove noncommutative reciprocity laws (i.e. the splitting of the central extensions over some subgroups) for arithmetic surfaces and projective surfaces over a finite field. These reciprocity laws connect central extensions which are constructed locally and globally.

30 pages; corrected typos; to appear in Izvestiya: Mathematics

References in corpus (1)

• Questions and Remarks to the Langlands Program

Cited by in corpus (4)

• On the $3$-representations of groups and the $2$-categorical Traces
• Central extensions and Riemann-Roch theorem on algebraic surfaces
• Arithmetic Central Extensions and Reciprocity Laws for Arithmetic Surface
• Noncommutative reciprocity laws on algebraic surfaces: a case of tame ramification