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

By J. Thorne. Journal of the Institute of Mathematics of Jussieu, 2011

119 citations recorded by the source corpus.

Abstract 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ad0c029a69959330246b5f41dfe551e878ac0a99

How researchers see this paper

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In Algebra and Number Theory

1. T. Gee
2. David Geraghty
3. Thomas Barnet-Lamb
4. Frank Calegari
5. M. Emerton
6. David Savitt
7. J. Thorne
8. C. Johansson

In Geometry and Topology

1. T. Gee
2. David Geraghty
3. Thomas Barnet-Lamb
4. J. Thorne
5. M. Emerton
6. David Savitt
7. M. Kisin
8. C. Johansson

In Mathematical Physics

1. T. Gee
2. David Geraghty
3. Thomas Barnet-Lamb
4. J. Thorne
5. M. Emerton
6. David Savitt
7. M. Kisin
8. C. Johansson

Citations in the corpus

• COMPANION FORMS FOR UNITARY AND SYMPLECTIC GROUPS (2010, background): “In particular, thanks to the work of Thorne ([Tho10]), one can slightly weaken the “big image” assumptions made in this paper.”
• Serre weights for rank two unitary groups (2011, methodology): “For the notion of an adequate subgroup of GL2(Fl), which was originally defined in [Tho10], we refer the reader to Appendix A, where a detailed discussion of this condition is given.”