1. Corps de nombres peu ramifies et formes automorphes autoduales
- Author
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Laurent Clozel, Gaëtan Chenevier, Centre de Mathématiques Laurent Schwartz (CMLS), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), and Chenevier, Gaetan
- Subjects
Trace (linear algebra) ,General Mathematics ,media_common.quotation_subject ,Mathematics::Number Theory ,01 natural sciences ,Combinatorics ,11R32, 11F70 ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,0101 mathematics ,Representation Theory (math.RT) ,[MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT] ,Mathematics::Representation Theory ,Finite set ,media_common ,Mathematics ,Mathematics - Number Theory ,[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] ,Applied Mathematics ,010102 general mathematics ,Algebraic extension ,16. Peace & justice ,Infinity ,Injective function ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Algebra ,010307 mathematical physics ,Mathematics - Representation Theory ,Symplectic geometry ,[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] - Abstract
Let S be a finite set of primes, p in S, and Q_S a maximal algebraic extension of Q unramified outside S and infinity. Assume that |S|>=2. We show that the natural maps Gal(Q_p^bar/Q_p) --> Gal(Q_S/Q) are injective. Much of the paper is devoted to the problem of constructing selfdual automorphic cuspidal representations of GL(2n,A_Q) with prescribed properties at all places, that we study via the twisted trace formula of J. Arthur. The techniques we develop shed also some lights on the orthogonal/symplectic alternative for selfdual representations of GL(2n)., 50 pages, french. Section 4.18 has been extended : let F be a totally real field and \pi a selfdual cuspidal automorphic representation of GL(2n,A_F) which is cohomological at all the archimedean places and discrete at a finite place at least, we show that for each place v the L-parameter of \pi_v preserves a non-degenerate symplectic pairing
- Published
- 2009