On the geometric Langlands conjecture

Frenkel, E.; Gaitsgory, D.; Vilonen, K.

doi:10.1090/S0894-0347-01-00388-5

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On the geometric Langlands conjecture

Authors: E. Frenkel, D. Gaitsgory and K. Vilonen
Journal: J. Amer. Math. Soc. 15 (2002), 367-417
MSC (2000): Primary 11R39, 11F70; Secondary 14H60, 22E55
Posted: December 31, 2001
MathSciNet review: 1887638
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Abstract: Let be a smooth, complete, geometrically connected curve over a field of characteristic . The geometric Langlands conjecture states that to each irreducible rank local system on one can attach a perverse sheaf on the moduli stack of rank bundles on (irreducible on each connected component), which is a Hecke eigensheaf with respect to . 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.

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