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

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Abstract

We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.

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Correspondence to Richard Taylor.

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Taylor, R. Automorphy for some l-adic lifts of automorphic mod l Galois representations. II. Publ.math.IHES 108, 183–239 (2008). https://doi.org/10.1007/s10240-008-0015-2

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  • DOI: https://doi.org/10.1007/s10240-008-0015-2

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