2000/12/27 by E. Frenkel, Edward Frenkel, Frenkel, E. +6
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0012255
openalex publication_date 2000/12/27 · arxiv created 2001/10/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth, complete, geometrically connected curve over a field of characteristic p. The geometric Langlands conjecture states that to each irreducible rank n local system E on X one can attach a perverse sheaf on the moduli stack of rank n bundles on X (irreducible on each connected component), which is a Hecke eigensheaf with respect to E. In this paper we derive the geometric Langlands conjecture from a certain vanishing conjecture. Furthermore, using recent results of Lafforgue, we prove this vanishing conjecture, and hence the geometric Langlands conjecture, in the case when the ground field is finite.