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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

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
Published electronically: December 31, 2001


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:
  • MathSciNet review: 1887638