Graduate Number Theory Seminar
Abel Castillo
UIC
On the analogy between elliptic curves and Drinfeld modules
Abstract: We will first recall some basic facts about torsion points of elliptic curves over $\mathbb Q$. Then, we will describe the function field setting, and define a Drinfeld module over $\mathbb F_q(T)$. We will then describe its torsion in the algebraic closure of $\mathbb F_q(T)$, and show how this gives rise to Galois representations similar to those coming from elliptic curves. As time permits, we will then state "open image" theorems in each setting, further reinforcing the analogy.
This talk is intended for an audience of graduate students interested in number theory.
Monday October 21, 2013 at 3:00 PM in SEO 612