Automorphy for some l -adic lifts of automorphic mod l Galois representations. II
Publications Mathématiques de l'IHÉS, Tome 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},
     mrnumber = {2470688},
     zbl = {1169.11021},
     language = {en},
     url = {http://www.numdam.org/articles/10.1007/s10240-008-0015-2/}
}
TY  - JOUR
AU  - Taylor, Richard
TI  - Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II
JO  - Publications Mathématiques de l'IHÉS
PY  - 2008
SP  - 183
EP  - 239
VL  - 108
PB  - Springer-Verlag
UR  - http://www.numdam.org/articles/10.1007/s10240-008-0015-2/
DO  - 10.1007/s10240-008-0015-2
LA  - en
ID  - PMIHES_2008__108__183_0
ER  - 
%0 Journal Article
%A Taylor, Richard
%T Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II
%J Publications Mathématiques de l'IHÉS
%D 2008
%P 183-239
%V 108
%I Springer-Verlag
%U http://www.numdam.org/articles/10.1007/s10240-008-0015-2/
%R 10.1007/s10240-008-0015-2
%G en
%F 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, Tome 108 (2008), pp. 183-239. doi : 10.1007/s10240-008-0015-2. http://www.numdam.org/articles/10.1007/s10240-008-0015-2/

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 | Zbl

2. C. Breuil, A. Mezard, Multiplicités modulaires et représentations de GL2(Z p ) et de Gal(𝐐 ¯ p /𝐐 p ) en ℓ=p , Duke Math. J. 115 (2002), p. 205-310 | MR | Zbl

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

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

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

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 | Zbl

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

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

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

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

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

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

Cité par Sources :