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Corps de nombres peu ramifiés et formes automorphes autoduales


Authors: G. Chenevier and L. Clozel
Journal: J. Amer. Math. Soc. 22 (2009), 467-519
MSC (2000): Primary 11F70, 11F72, 11F80
DOI: https://doi.org/10.1090/S0894-0347-08-00617-6
Published electronically: September 17, 2008
MathSciNet review: 2476781
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Abstract: 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 $ \vert S\vert\geq 2$. We show that the natural maps

$\displaystyle \operatorname{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p) \rightarrow \operatorname{Gal}(\mathbb{Q}_S/\mathbb{Q})$

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)$.


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Additional Information

G. Chenevier
Affiliation: Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris 13, 99 Av. J-B. Clément, 93430 Villetaneuse, France

L. Clozel
Affiliation: Centre d’Orsay Mathematique, Université Paris XI, Batiment 425, 91405 Orsay Cedex France

DOI: https://doi.org/10.1090/S0894-0347-08-00617-6
Received by editor(s): January 1, 1928
Received by editor(s) in revised form: January 1, 2007
Published electronically: September 17, 2008
Additional Notes: Le deuxième auteur est un membre de l’Institut Universitaire de France
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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