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

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Abstract

We extend the methods of Wiles and of Taylor and Wiles from GL2 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 GL2. 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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Authors and Affiliations

  1. Mathématique, Université Paris-Sud, Bât. 425, 91405, Orsay Cedex, France

    Laurent Clozel

  2. Institut de Mathématiques de Jussieu, U.M.R. 7586 du CNRS, 2, place Jussieu, 75251, Paris Cedex 05, France

    Michael Harris

  3. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Richard Taylor

Authors
  1. Laurent Clozel
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  2. Michael Harris
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  3. Richard Taylor
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Correspondence to Richard Taylor.

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Clozel, L., Harris, M. & Taylor, R. Automorphy for some l-adic lifts of automorphic mod l Galois representations . Publ.math.IHES 108, 1–181 (2008). https://doi.org/10.1007/s10240-008-0016-1

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