# Automorphy for Some $$l$$-Adic Lifts of Automorphic Mod $$l$$ Galois Representations

 dc.contributor.author Clozel, Laurent dc.contributor.author Taylor, Richard dc.contributor.author Harris, Michael dc.date.accessioned 2008-12-15T19:11:25Z dc.date.issued 2008 dc.identifier.citation Cozel, 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/. en dc.identifier.issn 1618-1913 dc.identifier.issn 0073-8301 en dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:2449392 dc.description.abstract 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), en 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. dc.description.sponsorship Mathematics en dc.publisher Springer Berlin / Heidelberg en dc.relation.isversionof http://www.springerlink.com/content/108804/ en dc.relation.isversionof http://dx.doi.org/10.1007/s10240-008-0016-1 en dash.license OAP dc.title Automorphy for Some $$l$$-Adic Lifts of Automorphic Mod $$l$$ Galois Representations en dc.relation.journal Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques en dash.depositing.author Taylor, Richard

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