Quantitative Equidistribution of Small Points for Canonical Heights

Abstract: Let $K$ be a number field and $A$ an abelian variety over $K$. Then if $h_{\operatorname{NT}}(x)$ denotes the Neron--Tate height of $x \in A(\overline{\mathbb{Q}})$, Szpiro-Ullmo-Zhang showed that the Galois orbits of a generic sequence $(x_n)$ with $h_{\operatorname{NT}}(x_n) \to 0$ must equidistribute to the Haar measure of $A(\mathbb{C})$. In this talk, I will explain a quantitative version of their equidistribution theorem along with its generalization to polarized dynamical systems.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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