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On the geometric Langlands conjecture |
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| Authors: | E. Frenkel D. Gaitsgory K. Vilonen |
| Affiliation: | Department of Mathematics, University of California, Berkeley, California 94720 D. Gaitsgory ; Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 K. Vilonen ; Department of Mathematics, Northwestern University, Evanston, Illinois 60208 |
| 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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