On the potential automorphy of certain odd-dimensional Galois representations

Details On the potential automorphy of certain odd-dimensional Galois representations On the potential automorphy of certain odd-dimensional Galois representations

2009-01-16

arxiv.org/abs/0901.2514v2

Compositio Mathematica (2010), 146: 607-620

Mathematics

Number Theory

13 pages. Essentially final version, to appear in Compositio Mathematica. This version does not incorporate minor changes (e.g

Scientific paper

10.1112/S0010437X09004527

In a previous paper, the potential automorphy of certain Galois representations to GL_n for n even was established, following work of Harris, Shepherd-Barron and Taylor and using the lifting theorems of Clozel, Harris and Taylor. In this paper, we extend those results to n=3 and n=5, and conditionally to all other odd n. The key additional tools necessary are results which give the automorphy or potential automorphy of symmetric powers of elliptic curves, most notably those of Gelbert, Jacquet, Kim, Shahidi and Harris.

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