Number Theory Seminar
Nathan Jones
University of Mississippi
Images of Galois representations associated to elliptic curves
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.
Friday April 27, 2012 at 12:00 PM in SEO 427