Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
Publications Mathématiques de l'IHÉS, Volume 108 (2008), pp. 183-239.

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.

@article{PMIHES_2008__108__183_0,
     author = {Taylor, Richard},
     title = {Automorphy for some l-adic lifts of automorphic mod l {Galois} representations. {II}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {183--239},
     publisher = {Springer-Verlag},
     volume = {108},
     year = {2008},
     doi = {10.1007/s10240-008-0015-2},
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     url = {http://www.numdam.org/articles/10.1007/s10240-008-0015-2/}
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Taylor, Richard. Automorphy for some l-adic lifts of automorphic mod l Galois representations. II. Publications Mathématiques de l'IHÉS, Volume 108 (2008), pp. 183-239. doi : 10.1007/s10240-008-0015-2. http://www.numdam.org/articles/10.1007/s10240-008-0015-2/

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