Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Wednesday, October 25th, 2017

Time: 1:30 p.m.  Place: Jeffery Hall 319

Speaker: Richard Leyland

Title: Galois representations of CM Elliptic Curves

Abstract: We introduce the notion of the mod-N Galois representation $\rho_{E/F,N}$ attached to an elliptic curve $E/F$. Motivated by conjectures of Frey and Mazur, we aim to determine all elliptic curves $E’/F$ such that $\rho_{E’/F,N}\cong \rho_{E/F,N}$ in the case where both $E$ and $E’$ have complex multiplication. In this talk, we introduce the problems, terminology currently being worked on and present a small result in the case where $E$ and $E’$ have complex multiplication by different imaginary quadratic fields.