Automorphy for some l-adic lifts of automorphic mod l Galois representations

Clozel, Laurent ; Harris, Michael ; Taylor, Richard

Publications Mathématiques de l'IHÉS, Tome 108 (2008), p. 1-181 / Harvested from Numdam

Résumé

We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles' method we show that this conjecture implies that our automorphy lifting theorem could be extended to cover lifts that are not minimally ramified.

Détail

Publié le : 2008-01-01

MR 2470687 | Zbl 1169.11020 | 2 citations dans Numdam

DOI : https://doi.org/10.1007/s10240-008-0016-1

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