Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2235-2325.

The aim of these notes is to generalize Laumon’s construction [20] 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 [11] 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 [11]

L’objectif de ces notes est de généraliser la construction de Laumon [20] des faisceaux automorphes correspondant aux systèmes locaux sur une courbe projective, lisse C aux cas des systèmes locaux ayant une ramification unipotente indécomposable en un nombre fini de points. Dans ce but, il est nécessaire d’étendre aux faisceaux cohérents la notion de structure parabolique des fibrés vectoriels. Une fois ceci défini, beaucoup d’arguments de l’article “On the geometric Langlands conjecture” de Frenkel, Gaitsgory et Vilonen [11] se transposent à notre situation. Nous montrons que nos faisceaux se descendent sur l’espace de modules des fibrés paraboliques si le rang est 3 et que le cas général peut se déduire d’une généralisation de la conjecture d’annulation de [11]

DOI: 10.5802/aif.2080
Classification: 11R39, 11F70, 14H60, 22E55
Keywords: parabolic vector bundles, automorphic sheaves, geometric Langlands correspondence
Mot clés : fibrés vectoriels paraboliques, faisceaux automorphes, correspondance de Langlands géométrique
Heinloth, Jochen 1

1 Universität Göttingen, Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen (Allemagne)
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Heinloth, Jochen. Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2235-2325. doi : 10.5802/aif.2080. https://aif.centre-mersenne.org/articles/10.5802/aif.2080/

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