On a vanishing conjecture appearing in the geometric Langlands correspondence

2002/04/07 by Dennis Gaitsgory, D. Gaitsgory, Gaitsgory, D. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/0204081

Revised version

openalex publication_date 2002/04/07 · arxiv created 2003/10/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth complete curve, and let Bun_n be the moduli stack of rank n vector bundles on X. Let E be a local system on X. In a recent paper of E.Frenkel, K.Vilonen and the author, it was shown that the vanishing of a certian functor Av_E^d acting from the category D(Bun_n) to itself, implies the geometric Langlands conjecture. In this paper we establish the required vanishing result. Our proof works for sheaves with char=0 coefficients, or with torsion coefficients when the parameter d is less than the characteristic.

Cited by

• Some results about the geometric Whittaker model

Related

• On the geometric Langlands conjecture
• Geometrization of the local Langlands correspondence
• The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support
• On automorphic sheaves on Bun_G
• Geometric Langlands in positive characteristic from characteristic zero