Geodesic
On the geometric Langlands conjecture
Frenkel, E.1 ; Gaitsgory, D.2 ; Vilonen, K.3
1 Department of Mathematics, University of California, Berkeley, California 94720
2 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
3 Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 367-417

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-01-00388-5

Frenkel, E. 1 ; Gaitsgory, D. 2 ; Vilonen, K. 3

1 Department of Mathematics, University of California, Berkeley, California 94720
2 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
3 Department of Mathematics, Northwestern University, Evanston, Illinois 60208 
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Frenkel, E.; Gaitsgory, D.; Vilonen, K. On the geometric Langlands conjecture. Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 367-417. doi: 10.1090/S0894-0347-01-00388-5

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