Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case
By R. Bezrukavnikov, Alexander Braverman. 2006
54 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f844f1ef5ad0072790928571100cce27ee2d3249
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Langlands duality for Hitchin systems (2006, methodology): “o get the full categorical duality Db c LHiggs ∼=Db c (Higgs), one can combine (7) with the duality for representations of commutative group stacks described in Arinkin’s appendix to [DP08] (see also [BeBra07]), or invoke the recent result [BB09] of O.Ben-Bassat. In fact, Ben-Bassat’s proof works in”
- Nonabelian Hodge theory in characteristic p (2005, background): “We would also like to thank Alexander Beilinson, Alexander Braverman, Luc Illusie, and Ofer Gabber for the interest they showed and the advice they provided.”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, methodology): “In addition, a geometric version of the Langlands program for curves has been much developed [4-8], both for curves over a field of characteristic p and for ordinary complex Riemann surfaces.”