Counting elliptic curves with a rational N-isogeny

Soumya Sankar (Ohio State University)

15-Nov-2022, 21:00-22:00 (16 months ago)

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

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