Colloquium Mathematics - Valentijn Karemaker, University of Utrecht

Title: Abelian varieties over finite fields

Abstract:

Abelian varieties are geometric objects that are described by polynomial equations. They moreover have the special feature that you can make sense of “adding” two points on the abelian variety to get a third point on it. As such, these varieties have rich arithmetic and geometric structures. We will study these varieties in characteristic p, that is, when arithmetic is modular. It turns out that the moduli space of all such abelian varieties has a lot of structure as well and admits various interesting stratifications.

I will discuss some ways in which abelian varieties and their moduli spaces have come up in my recent research.