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Corps de nombres peu ramifies et formes automorphes autoduales
- Source :
- Journal of the American Mathematical Society, Journal of the American Mathematical Society, American Mathematical Society, 2009, 22 (2), pp.467-519
- Publication Year :
- 2009
- Publisher :
- HAL CCSD, 2009.
-
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).<br />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
- 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]
Subjects
Details
- Language :
- French
- ISSN :
- 08940347
- Database :
- OpenAIRE
- Journal :
- Journal of the American Mathematical Society, Journal of the American Mathematical Society, American Mathematical Society, 2009, 22 (2), pp.467-519
- Accession number :
- edsair.doi.dedup.....03031121381775c762a1e960aa0bbd79