Abstract
AbstractIn a previous paper, the potential automorphy of certain Galois representations to GLn for n even was established, following the 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.
Subject
Algebra and Number Theory
Reference14 articles.
1. Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
2. Cuspidality of symmetric powers with applications;Kim;Duke Math. J.,2002
3. [14] Taylor R. , Automorphy for some l-adic lifts of automorphic mod l Galois representations. II, Preprint (2006).
4. [5] Harris M. , Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications, in Algebra, arithmetic and geometry–Manin festschrift, Progress in Mathematics (Birkhäuser, Boston, MA, 2007) (to appear).
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献