2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137950Let 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 πa 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 π_v preserves a non-degenerate symplectic pairingNumber TheoryRepresentation Theory11R32, 11F70text