Number Theory Seminar

Date: April 9, 2024

Time: 09:45AM - 10:45AM

Location: BLOC 302

Speaker: Zhining Wei, Brown University

Title: Effective Open Image Theorem for pairs of elliptic curves

Abstract: In 1972, Serre proved the celebrated Open Image Theorem, claiming that for a non-CM elliptic curve E over Q, the residue modulo $\ell$ Galois representation associated with E is surjective for sufficiently large prime $\ell$. An effective version of this theorem seeks to bound such least non-surjective prime $\ell$. In the talk, I will review some results concerning the effective version of Serre's Open Image Theorem. Then, I will present a work in progress on the effective open image theorem for pairs of elliptic curves, especially the semistable elliptic curves. This is joint with Tian Wang.