Nathan Jones : Images of Galois representations associated to elliptic curves

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

April 27, 2012, noon

In

SEO 427

Abstract

Given an elliptic curve E defined over a number field K, consider the action of the absolute Galois group of K on the n-torsion of E. This defines a Galois representation into GL_2(Z/n Z). It is of fundamental interest to understand the image of this representation, as illustrated by the now classical complex multiplication theory and by Serre's study of ell-adic representations. In this talk I will survey some results on this topic, highlighting the situation for a ``typical'' elliptic curve. I will also discuss how this typical behavior allows for applications to studies of families of elliptic curves.