Automorphy for Some \(l\)-Adic Lifts of Automorphic Mod \(l\) Galois Representations
Harris, MichaelNote: Order does not necessarily reflect citation order of authors.
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CitationCozel, Laurent, Michael Harris, and Richard Taylor. 2008. Automorphy of some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques. Online First (November), http://www.springerlink.com/content/108804/.
AbstractWe 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.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2449392
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