Speaker: Borys Kadets (Hebrew University)

Title: Groups of points on abelian and Jacobian varieties over finite fields

Abstract:

I will describe various results, some old and some new, on the structure of the group of points of an abelian variety over a finite field. The talk will focus on the case of varieties of large dimension over a fixed finite field. In this regime the point-counts are controlled by elementary, but nontrivial, questions on distributions of algebraic numbers. The group structure is harder to control: the Weil bounds allow for the possibility of the exponent of the group staying bounded as the dimension grows. I will explain that at least in the case of Jacobians this cannot be the case. Part of the talk is based on recent joint work with Daniel Keliher.