JournalscmhVol. 81, No. 2pp. 449–470

Sur la compatibilité entre les correspondances de Langlands locale et globale pour U(3)

  • Joël Bellaïche

    Columbia University, New York, United States
Sur la compatibilité entre les correspondances de Langlands locale et globale pour U(3) cover
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Abstract

Using a level-raising argument (and a result of Larsen on the image of Galois representations in compatible systems), we prove that for any automorphic representation π\pi for U(3), the l-adic Galois representation ρl\rho_l which is attached to π\pi by the work of Blasius and Rogawski is the one expected by local Langlands correspondance at every finite place (at least up to semi-simplification and for a density one set of primes l). We rely on the work of Harris and Taylor, who have proved the same results (for U(n)) assuming the base change of π\pi is square-integrable at one place. As a corollary, every automorphic representation which is tempered at an infinite number of places is tempered at all places.

Cite this article

Joël Bellaïche, Sur la compatibilité entre les correspondances de Langlands locale et globale pour U(3). Comment. Math. Helv. 81 (2006), no. 2, pp. 449–470

DOI 10.4171/CMH/58