Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems

Details Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems

2003-02-18

arxiv.org/abs/math/0302210v1

Mathematics

Algebraic Geometry

60 pages

Scientific paper

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 $\leq 3$ and that the general case can be deduced form a generalization of the vanishing conjecture of [10].

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