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

We extend the methods of Wiles and of Taylor and Wiles from GL 2 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 an...

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Veröffentlicht in:Publications mathématiques. Institut des hautes études scientifiques 2008-11, Vol.108 (1), p.1-181
Hauptverfasser: Clozel, Laurent, Harris, Michael, Taylor, Richard
Format: Artikel
Sprache:eng
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Zusammenfassung:We extend the methods of Wiles and of Taylor and Wiles from GL 2 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 GL 2 . 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.
ISSN:0073-8301
1618-1913
DOI:10.1007/s10240-008-0016-1