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On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne

  • Jack Thorne (a1)

We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into GLn. Existing theorems require that the residual representation have ‘big’ image, in a certain technical sense. Our theorems are based on a strengthening of the Taylor–Wiles method which allows one to weaken this hypothesis.

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1. T. Barnet-Lamb , T. Gee and D. Geraghty , The Sato–Tate conjecture for Hilbert modular forms, J. Am. Math. Soc. 24 (2011), 411469.

10. L. Clozel , M. Harris and R. Taylor , Automorphy for some l-adic lifts of automorphic mod l Galois representations (with Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by M.-F. Vignéras, Publ. Math. IHES 108 (2008), 1181.

12. T. Gee , Automorphic lifts of prescribed types, Math. Annalen 350(1) (2011), 107144.

16. B. H. Gross , Algebraic modular forms, Israel J. Math. 113 (1999), 6193.

18. R. M. Guralnick , Small representations are completely reducible, J. Alg. 220(2) (1999), 531541.

22. M. Kisin , Potentially semi-stable deformation rings, J. Am. Math. Soc. 21(2) (2008), 513546.

23. G. Kuperberg , Denseness and Zariski denseness of Jones braid representations, Geom. Topol. 15 (2011), 1139.

25. J. M. Lansky , Parahoric fixed spaces in unramified principal series representations, Pac. J. Math. 204(2) (2002), 433443.

26. M. Larsen and R. Pink , Finite subgroups of algebraic groups, J. Am. Math. Soc. 24(4) (2011), 11051158.

27. W. Magnus , On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7 (1954), 649673.

33. J.-P. Serre , Sur la semi-simplicité des produits tensoriels de représentations de groupes, Invent. Math. 116 (1994), 513530. (13)

34. J. A. Shalika , The multiplicity one theorem for GLn, Annals Math. 100 (1974), 171193.

35. S. W. Shin , Galois representations arising from some compact Shimura varieties, Annals Math. 173 (2011), 16451741.

36. T. A. Springer , Twisted conjugacy in simply connected groups, Transform. Groups 11(3) (2006), 539545.

38. R. Steinberg , Automorphisms of classical Lie algebras, Pac. J. Math. 11 (1961), 11191129.

41. R. Taylor , Automorphy for some l-adic lifts of automorphic mod l Galois representations, II, Publ. Math. IHES 108 (2008), 183239.

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
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