Counting elliptic curves with a rational N-isogeny
Soumya Sankar (Ohio State University)
Abstract: The classical problem of counting elliptic curves with a rational N-isogeny can be phrased in terms of counting rational points on certain moduli stacks of elliptic curves. Counting points on stacks poses various challenges, and I will discuss these along with a few ways to overcome them. I will also talk about height functions on certain stacks, focusing on the theory of heights on stacks developed in recent work of Ellenberg, Satriano and Zureick-Brown. I will then use their framework to count elliptic curves with an N-isogeny for certain N. The talk assumes no prior knowledge of stacks and is based on joint work with Brandon Boggess.
number theory
Audience: researchers in the topic
University of Arizona Algebra and Number Theory Seminar
Organizers: | Aparna Upadhyay*, Pan Yan* |
*contact for this listing |