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Inventiones mathematicae

, Volume 139, Issue 2, pp 439–455 | Cite as

Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

  • Guy Henniart
Article

Abstract.

Let F be a finite extension of ℚ p . For each integer n≥1, we construct a bijection from the set ?F0(n) of isomorphism classes of irreducible degree n representations of the (absolute) Weil group of F, onto the set ? F 0 (n) of isomorphism classes of smooth irreducible supercuspidal representations of GL n (F). Those bijections preserve epsilon factors for pairs and hence we obtain a proof of the Langlands conjectures for GL n over F, which is more direct than Harris and Taylor’s. Our approach is global, and analogous to the derivation of local class field theory from global class field theory. We start with a result of Kottwitz and Clozel on the good reduction of some Shimura varieties and we use a trick of Harris, who constructs non-Galois automorphic induction in certain cases.

Mathematics Subject Classification (1991): 11F70, 11R39, 11S37, 22E50, 22E55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Guy Henniart
    • 1
  1. 1.Département de Mathématiques, UMR 8628 du CNRS, bât. 425, Université de Paris-Sud, F-91405 Orsay Cedex, France (e-mail: Guy.Henniart@math.u-psud.fr)France

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