Automorphy for some l-adic lifts of automorphic mod l Galois representations
Publications Mathématiques de l'IHÉS, Volume 108 (2008), p. 1-181

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.

@article{PMIHES_2008__108__1_0,
     author = {Clozel, Laurent and Harris, Michael and Taylor, Richard},
     title = {Automorphy for some l-adic lifts of automorphic mod l Galois representations},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer-Verlag},
     volume = {108},
     year = {2008},
     pages = {1-181},
     doi = {10.1007/s10240-008-0016-1},
     zbl = {1169.11020},
     mrnumber = {2470687},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2008__108__1_0}
}
Clozel, Laurent; Harris, Michael; Taylor, Richard. Automorphy for some l-adic lifts of automorphic mod l Galois representations. Publications Mathématiques de l'IHÉS, Volume 108 (2008) pp. 1-181. doi : 10.1007/s10240-008-0016-1. http://www.numdam.org/item/PMIHES_2008__108__1_0/

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