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

Jochen Heinloth[1]

  • [1] Universität Göttingen, Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen (Allemagne)

Annales de l'Institut Fourier (2004)

  • Volume: 54, Issue: 7, page 2235-2325
  • ISSN: 0373-0956

Abstract

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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]

How to cite

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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 54.7 (2004): 2235-2325. <http://eudml.org/doc/116173>.

@article{Heinloth2004,
abstract = {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 $\le 3$ and that the general case can be deduced form a generalization of the vanishing conjecture of [11]},
affiliation = {Universität Göttingen, Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen (Allemagne)},
author = {Heinloth, Jochen},
journal = {Annales de l'Institut Fourier},
keywords = {parabolic vector bundles; automorphic sheaves; geometric Langlands correspondence},
language = {eng},
number = {7},
pages = {2235-2325},
publisher = {Association des Annales de l'Institut Fourier},
title = {Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems},
url = {http://eudml.org/doc/116173},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Heinloth, Jochen
TI - Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
JO - Annales de l'Institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 7
SP - 2235
EP - 2325
AB - 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 $\le 3$ and that the general case can be deduced form a generalization of the vanishing conjecture of [11]
LA - eng
KW - parabolic vector bundles; automorphic sheaves; geometric Langlands correspondence
UR - http://eudml.org/doc/116173
ER -

References

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