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On the geometric Langlands conjecture

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

E. Frenkel
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

D. Gaitsgory
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

K. Vilonen
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208

DOI: 10.1090/S0894-0347-01-00388-5
PII: S 0894-0347(01)00388-5
Received by editor(s): February 14, 2001
Posted: December 31, 2001
Copyright of article: Copyright 2001, by E. Frenkel, D. Gaitsgory, K. Vilonen

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