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 |
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Hauptverfasser: | , , |
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. |
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ISSN: | 0073-8301 1618-1913 |
DOI: | 10.1007/s10240-008-0016-1 |