P-adic uniformization of modular elliptic curves over number fields

Speaker: Haluk Sengun, University of Sheffield

Date: Monday, March 23rd

Time: 4:00pm

Location: Seminar Room, Ag 1.01

Abstract:

The Langlands Programme predicts that a weight 2 newform f over a number field K with integer Hecke eigenvalues generally should have an "associated" elliptic curve E_f over K. When K is the rationals, this is celebrated work of Shimura, and when K is totally real, in many cases, this prediction holds true via an application of the Jacquet-Langlands transfer. However for general K, w are at a loss in associating elliptic curves to weight 2 newforms. Together with X.Guitart (Barcelona) and M.Masdeu (Warwick), we associated, building crucially on works of H.Darmon and of M.Greenberg, a p-adic lattice L to f, under certain hypothesis, and implicitly conjectured that L is commensurable with the p-adic Tate lattice of E_f. In this talk, I will present this conjecture in detail and discuss how it can be used to compute, directly from f, an explicit Weierstrass equation for the conjectural E

Algebra & Number Theory 2014_15