Jacob Mayle : Serre's Open image Theorem and Beyond

Posted by Nathan Jones , part of the Number Theory Seminar.

At

Jan. 14, 2022, 1 p.m.

In

Zoom

Abstract

Let E/Q be an elliptic curve. For each prime number ell, one considers the mod ell Galois representation of E, which encodes the action of the absolute Galois group of Q on the ell-torsion subgroup of E. In 1972, Serre showed that if E is without complex multiplication, then the mod ell Galois representation is surjective whenever ell is sufficiently large. In this talk, we'll discuss the theorem, as well as recent computational and theoretical progress related to it.