Corps de nombres peu ramifies et formes automorphes autoduales

Details Corps de nombres peu ramifies et formes automorphes autoduales Corps de nombres peu ramifies et formes automorphes autoduales

2007-06-22

arxiv.org/abs/0706.3336v2

Mathematics

Number Theory

50 pages, french. Section 4.18 has been extended : let F be a totally real field and \pi a selfdual cuspidal automorphic repre

Scientific paper

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).

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