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

Publications Mathématiques de l'IHÉS (2008)

- Volume: 108, page 183-239
- ISSN: 0073-8301

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topTaylor, Richard. "Automorphy for some l-adic lifts of automorphic mod l Galois representations. II." Publications Mathématiques de l'IHÉS 108 (2008): 183-239. <http://eudml.org/doc/274396>.

@article{Taylor2008,

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.},

author = {Taylor, Richard},

journal = {Publications Mathématiques de l'IHÉS},

keywords = {modularity of lifts of Galois representations; minimality condition; Sato-Tate conjecture},

language = {eng},

pages = {183-239},

publisher = {Springer-Verlag},

title = {Automorphy for some l-adic lifts of automorphic mod l Galois representations. II},

url = {http://eudml.org/doc/274396},

volume = {108},

year = {2008},

}

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

PB - Springer-Verlag

VL - 108

SP - 183

EP - 239

AB - 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.

LA - eng

KW - modularity of lifts of Galois representations; minimality condition; Sato-Tate conjecture

UR - http://eudml.org/doc/274396

ER -

## References

top- 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. Zbl0682.10022MR1007299
- 2. C. Breuil, A. Mezard, Multiplicités modulaires et représentations de GL2(Z p ) et de $Gal({\overline{\mathbf{Q}}}_{p}/{\mathbf{Q}}_{p})$ en ℓ=p, Duke Math. J.115 (2002), p. 205-310 Zbl1042.11030MR1944572
- 3. L. Clozel, M. Harris, and R. Taylor, Automorphy for some ℓ-adic lifts of automorphic mod ℓ Galois representations, this volume. Zbl1169.11021
- 4. D. Eisenbud, Commutative Algebra with a View Towards Algebraic Geometry, Springer, 1994. Zbl0819.13001MR1322960
- 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). Zbl0144.19904
- 6. M. Harris, N. Shepherd-Barron, and R. Taylor, Ihara’s lemma and potential automorphy, Ann. Math., to appear. Zbl1263.11061
- 7. M. Harris and R. Taylor, The Geometry and Cohomology of some Simple Shimura Varieties, Ann. Math. Stud., vol. 151, Princeton University Press, 2001. Zbl1036.11027MR1876802
- 8. M. Kisin, Moduli of finite flat groups schemes and modularity, Ann. Math., to appear. Zbl1201.14034MR2600871
- 9. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986. Zbl0603.13001MR879273
- 10. C. Skinner, A. Wiles, Base change and a problem of Serre, Duke Math. J.107 (2001), p. 15-25 Zbl1016.11017MR1815248
- 11. R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. Math.141 (1995), p. 553-572 Zbl0823.11030MR1333036
- 12. R. Taylor, T. Yoshida, Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc.20 (2007), p. 467-493 Zbl1210.11118MR2276777
- 13. A. Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. Math.141 (1995), p. 443-551 Zbl0823.11029MR1333035

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