Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
Publications Mathématiques de l'IHÉS, Volume 108  (2008), p. 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},
publisher = {Springer-Verlag},
volume = {108},
year = {2008},
pages = {183-239},
doi = {10.1007/s10240-008-0015-2},
zbl = {1169.11021},
mrnumber = {2470688},
language = {en},
url = {http://www.numdam.org/item/PMIHES_2008__108__183_0}
}

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/item/PMIHES_2008__108__183_0/

1. J. Arthur and L. Clozel, Simple Algebras, Base Change and the Advanced Theory of the Trace Formula, Ann. Math. Stud., vol. 120, Princeton University Press, 1989. | MR 1007299 | Zbl 0682.10022

2. C. Breuil, A. Mezard, Multiplicités modulaires et représentations de GL2(Z p ) et de $Gal\left({\overline{𝐐}}_{p}/{𝐐}_{p}\right)$ en ℓ=p , Duke Math. J. 115 (2002), p. 205-310 | MR 1944572 | Zbl 1042.11030

3. L. Clozel, M. Harris, and R. Taylor, Automorphy for some ℓ-adic lifts of automorphic mod ℓ Galois representations, this volume. | Zbl 1169.11021

4. D. Eisenbud, Commutative Algebra with a View Towards Algebraic Geometry, Springer, 1994. | MR 1322960 | Zbl 0819.13001

5. A. Grothendieck, Eléments de géométrie algébrique. IV. Etude locale des schémas et des morphismes de schémas. III., Publ. Math., Inst. Hautes Étud. Sci., 28 (1966). | Numdam | Zbl 0144.19904

6. M. Harris, N. Shepherd-Barron, and R. Taylor, Ihara's lemma and potential automorphy, Ann. Math., to appear.

7. M. Harris and R. Taylor, The Geometry and Cohomology of some Simple Shimura Varieties, Ann. Math. Stud., vol. 151, Princeton University Press, 2001. | MR 1876802 | Zbl 1036.11027

8. M. Kisin, Moduli of finite flat groups schemes and modularity, Ann. Math., to appear. | MR 2600871 | Zbl 1201.14034

9. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986. | MR 879273 | Zbl 0603.13001

10. C. Skinner, A. Wiles, Base change and a problem of Serre, Duke Math. J. 107 (2001), p. 15-25 | MR 1815248 | Zbl 1016.11017

11. R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. Math. 141 (1995), p. 553-572 | MR 1333036 | Zbl 0823.11030

12. R. Taylor, T. Yoshida, Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc. 20 (2007), p. 467-493 | MR 2276777 | Zbl 1210.11118

13. A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. Math. 141 (1995), p. 443-551 | MR 1333035 | Zbl 0823.11029