Quantitative Equidistribution of Small Points for Canonical Heights

Let K be a number field with algebraic closure L and A an abelian variety over K. Then if (x_n) is a generic sequence of points of A(L) with Neron-Tate height tending to 0, Szpiro-Ullmo-Zhang proved that the Galois orbits of x_n converges weakly to the Haar measure of A. Yuan then generalized Szpiro-Ullmo-Zhang’s result to the setting of polarized endomorphisms on a projective variety X defined over K. In this talk, I will explain how to prove a quantitative version of Yuan’s result when X is assumed to be smooth. This was previously only known when dim X = 1.

There will be a pretalk on background material for the seminar talk from 2:00-2:45pm in SC 530. We especially encourage younger students to attend and ask questions!

Pretalk: I will talk about intersection theory on arithmetic surfaces and explain how Zhang proves the Bogomolov conjecture for curves in tori using the arithmetic analogs of classical results on surfaces (Hodge index, Hilbert-Samuel etc.)

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For more info, see https://researchseminars.org/seminar/HarvardNT