#### Conference abstracts

Session A3 - Computational Number Theory

July 10, 17:00 ~ 17:40

## Rational points on high genus curves over finite fields

### Alp Bassa

### Bogazici University, Turkey - alp.bassa@boun.edu.tr

In this talk we will be concerned with rational points on algebraic curves over finite fields. The central result in this area is without doubt the Hasseâ€”Weil Theorem, which implies strong bounds on the number of rational points. As noticed by Ihara, for curves of large genus this bound can be improved significantly. We will be interested in the question of how many rational points a high genus curve over a finite field can have. We will introduce several approaches to this problem and present a recent result (joint work with Beelen, Garcia, Stichtenoth) which provides strong lower bounds for the maximal possible number of rational points on curves over non-prime finite fields.

Joint work with Peter Beelen (DTU), Arnaldo Garcia (IMPA) and Henning Stichtenoth (Sabanci University).