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

Richard Taylor

Publications Mathématiques de l'IHÉS (2008)

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

Abstract

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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.

How to cite

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Taylor, 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

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  1. 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. 2. C. Breuil, A. Mezard, Multiplicités modulaires et représentations de GL2(Z p ) et de G a l ( 𝐐 ¯ p / 𝐐 p ) en ℓ=p, Duke Math. J.115 (2002), p. 205-310 Zbl1042.11030MR1944572
  3. 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. 4. D. Eisenbud, Commutative Algebra with a View Towards Algebraic Geometry, Springer, 1994. Zbl0819.13001MR1322960
  5. 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. 6. M. Harris, N. Shepherd-Barron, and R. Taylor, Ihara’s lemma and potential automorphy, Ann. Math., to appear. Zbl1263.11061
  7. 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. 8. M. Kisin, Moduli of finite flat groups schemes and modularity, Ann. Math., to appear. Zbl1201.14034MR2600871
  9. 9. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986. Zbl0603.13001MR879273
  10. 10. C. Skinner, A. Wiles, Base change and a problem of Serre, Duke Math. J.107 (2001), p. 15-25 Zbl1016.11017MR1815248
  11. 11. R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. Math.141 (1995), p. 553-572 Zbl0823.11030MR1333036
  12. 12. R. Taylor, T. Yoshida, Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc.20 (2007), p. 467-493 Zbl1210.11118MR2276777
  13. 13. A. Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. Math.141 (1995), p. 443-551 Zbl0823.11029MR1333035

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