## Works of Frenkel, Gaitsgory et Vilonen on the Drinfeld-Langlands correspondence and Drinfeld-Langlands. (Travaux de Frenkel, Gaitsgory et Vilonen sur la correspondence de Drinfeld-Langlands.)(French)Zbl 1161.11360

Séminaire Bourbaki. Volume 2001/2002. Exposés 894–908. Paris: Société Mathématique de France (ISBN 2-85629-149-X/pbk). Astérisque 290, 267-284, Exp. No. 906 (2003).
Summary: In 1967, Langlands conjectured a natural correspondence between automorphic representations and Galois representations, over number fields as well as over function fields. In 1983, Drinfeld discovered a geometric analog of the Langlands correspondence in the function field case, which extends the geometric class field theory of Lang and Rosenlicht. The so called Drinfeld-Langlands correspondence is a conjectural duality between two moduli spaces that are naturally associated to an algebraic curve $$X$$ and a reductive group $$G$$. When $$X$$ is projective and $$G$$ is the full linear group $$\text{GL}(n)$$, a large part of this correspondence has recently been established by E. Frenkel, D. Gaitsgory and K. Vilonen [J. Am. Math. Soc. 15, No. 2, 367–417 (2002; Zbl 1071.11039)].
For the entire collection see [Zbl 1050.00006].

### MSC:

 11G45 Geometric class field theory 11R39 Langlands-Weil conjectures, nonabelian class field theory 14H60 Vector bundles on curves and their moduli 11F70 Representation-theoretic methods; automorphic representations over local and global fields

Zbl 1071.11039
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