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, while posing various challenges, has also opened up several new avenues of exploration in the last few years. In this talk, I will give an introduction to modular curves from the stacky perspective, discuss some notions of height on them, and use some of these notions to answer the counting question mentioned above. Time permitting, I will talk about this in the context of the stacky version of the Batyrev-Manin conjecture. The talk assumes no prior knowledge of stacks and is based on joint work with Brandon Boggess.

algebraic geometrynumber theory

Audience: researchers in the topic

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FGC-HRI-IPM Number Theory Webinars

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