Corps de nombres peu ramifiés et formes automorphes autoduales

Chenevier, G.¹ ; Clozel, L.²

¹ Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris 13, 99 Av. J-B. Clément, 93430 Villetaneuse, France
² Centre d’Orsay Mathematique, Université Paris XI, Batiment 425, 91405 Orsay Cedex France

Journal of the American Mathematical Society, Tome 22 (2009) no. 2, pp. 467-519

Résumé

Let $S$ be a finite set of primes, $p$ in $S$, and $\mathbb {Q}_S$ a maximal algebraic extension of $\mathbb {Q}$ unramified outside $S$ and $\infty$. Assume that $|S|\geq 2$. We show that the natural maps \[ \operatorname {Gal}(\overline {\mathbb {Q}_p}/\mathbb {Q}_p) \rightarrow \operatorname {Gal}(\mathbb {Q}_S/\mathbb {Q})\] are injective. Much of the paper is devoted to the problem of constructing self-dual automorphic cuspidal representations of $\operatorname {GL}(2n,\mathbb {A}_{\mathbb {Q}})$ with prescribed properties at all places, which we study via Arthur’s twisted trace formula. The techniques we develop also shed some light on the orthogonal/symplectic alternative for self-dual representations of $\operatorname {GL}(2n)$.

Détail

DOI : 10.1090/S0894-0347-08-00617-6

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