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

 Title: Automorphy for Some $$l$$-Adic Lifts of Automorphic Mod $$l$$ Galois Representations Author: Clozel, Laurent; Taylor, Richard; Harris, Michael Note: Order does not necessarily reflect citation order of authors. 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/. Full Text & Related Files: Clozel_Automorphy.pdf (942.5Kb; PDF) 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), 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. Published Version: http://www.springerlink.com/content/108804/ Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2449392 Downloads of this work: