2003/02/18 by Jochen Heinloth, Heinloth, Jochen · 2 citations
Mathematics · #11R39 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:11R39 #msc:14H60
paper · pdf · doi:10.48550/arxiv.math/0302210
60 pages
arxiv created 2003/02/18 · openalex publication_date 2003/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of these notes is to generalize Laumon's construction [18] of automorphic sheaves corresponding to local systems on a smooth, projective curve C to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article "On the geometric Langlands conjecture" by Frenkel, Gaitsgory and Vilonen [10] carry over to our situation. We show that our sheaves descend to the moduli space of parabolic bundles if the rank is ≤ 3 and that the general case can be deduced form a generalization of the vanishing conjecture of [10].