Conference abstracts

Session S07 - Finite Fields

July 28, 18:00 ~ 18:25

## The distribution of points on families of curves over finite fields

### Matilde Lalín

### Université de Montréal, Canada - mlalin@dms.umontreal.ca

We give an overview of a general trend of results that say that the distribution of the number of $\mathbb{F}_q$-points of certain families of curves of genus $g$ is asymptotically given by a sum of $q+1$ independent identically distributed random variables as $g$ goes to infinity. In particular, we discuss the distribution of the number of $\mathbb{F}_q$-points for cyclic $\ell$-covers of genus $g$. This work generalizes previous results in which only connected components of the moduli space were considered.