Travaux de Frenkel, Gaitsgory et Vilonen sur la correspondance de Drinfeld-Langlands

Abstract

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 GL(n), a large part of this correspondence has recently been established by E. Frenkel, D. Gaitsgory et K. Vilonen.