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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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On the geometric Langlands conjecture
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by E. Frenkel, D. Gaitsgory and K. Vilonen
J. Amer. Math. Soc. 15 (2002), 367-417
DOI: https://doi.org/10.1090/S0894-0347-01-00388-5
Published electronically: 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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Bibliographic Information
  • E. Frenkel
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 257624
  • ORCID: 0000-0001-6519-8132
  • D. Gaitsgory
  • Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
  • K. Vilonen
  • Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
  • MR Author ID: 178620
  • Received by editor(s): February 14, 2001
  • Published electronically: December 31, 2001
  • © Copyright 2001 by E. Frenkel, D. Gaitsgory, K. Vilonen
  • Journal: J. Amer. Math. Soc. 15 (2002), 367-417
  • MSC (2000): Primary 11R39, 11F70; Secondary 14H60, 22E55
  • DOI: https://doi.org/10.1090/S0894-0347-01-00388-5
  • MathSciNet review: 1887638