caa a22 4500 475738179 CHVBK 20180406123452.0 cr unu---uuuuu 170329e20000201xx s 000 0 fre 10.1007/s002220050012 doi (NATIONALLICENCE)springer-10.1007/s002220050012 Henniart Guy 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 aut Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique [Elektronische Daten] [Guy Henniart] Abstract. : Let F be a finite extension of ℚ p . For each integer n≥1, we construct a bijection from the set ?F 0 (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. Springer-Verlag Berlin Heidelberg, 2000 Mathematics Subject Classification (1991): 11F70, 11R39, 11S37, 22E50, 22E55 nationallicence Inventiones mathematicae Springer Berlin Heidelberg 139/2(2000-02-01), 439-455 0020-9910 139:2<439 2000 139 222 https://doi.org/10.1007/s002220050012 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220050012 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Henniart Guy 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 aut NATIONALLICENCE 773 0- Inventiones mathematicae Springer Berlin Heidelberg 139/2(2000-02-01), 439-455 0020-9910 139:2<439 2000 139 222 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer