Distribution, Height Density, and Propagation of Rational Points on Algebraic Varieties

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Joseph Silverman (Brown University)

Time：

Fri., 10:00-11:00 am, Oct. 18, 2024

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title：

Distribution, Height Density, and Propagation of Rational Points on Algebraic Varieties

Abstract：

I will start by describing a 30-year old trichotomy conjecture for the height density of rational points on varieties. I will then explain how it suggests various orbit propagation conjectures asserting, roughly, that a single Zariski dense orbit of rational points implies the existence of many such orbits. As time permits, I will explain the proofs of some of these conjectures for projective spaces, abelian varieties, and surfaces. (Joint work with Hector Pasten)