Ananth Shankar : Unlikely intersections and abelian varieties not isogenous to Jacobians

Posted by Nicole Looper , part of the Unlikely Intersections Seminar.

At

Sept. 26, 2023, 2 p.m.

In

636 SEO

Abstract

I will talk about the folklore question of whether there exist abelian varieties (of dimension $\geq4$) not isogenous to Jacobians, in the context of unlikely intersections. I will also touch upon how this question relates to the André--Oort conjecture (now, a theorem). If time permits, I will describe why we expect unlikely intersections to occur over $\overline{\mathbb{F}_p}$, even though we don't expect unlikely intersections in characteristic zero.