Number Theory Seminar
Soumya Sankar
Ohio State
Counting points on stacks and elliptic curves with a rational N-isogeny
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 the theory
of heights on stacks developed in work of Ellenberg, Satriano and Zureick-Brown, among others, and use it 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. Time permitting, I will also talk about ongoing work with Jennifer
Park on counting elliptic curves of higher degree.
Please note this talk is on Zoom. Link: https://uic.zoom.us/j/83309314462?pwd=K0xPMmVmQTB1WDMwQTkwRGZrVSs2dz09
Friday March 17, 2023 at 1:00 PM in Zoom