Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case

Details Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case

2006-02-12

arxiv.org/abs/math/0602255v2

Pure Appl. Math. Q. 3 (2007), no. 1, Special Issue: In honor of Robert D. MacPherson. Part 3, 153-179

Mathematics

Algebraic Geometry

Dedicated to R.MacPherson on the occasion of his 60th birthday

Scientific paper

Let X be a smooth projective curve over an algebraically closed field k of characteristic p>0. In this paper we explore the relation between algebraic D-modules on the moduli space $Bun_n$ of vector bundles of rank n on X and coherent sheaves on the moduli space $Loc_n$ of vector bundles endowed with a connection (in the way predicted by Beilinson and Drinfeld for k of characteristic 0). The main technical tools used in the paper are the geometry of the Hitchin system and the Azumaya property of the algebra of differential operators in characteristic p.

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