Curves over finite fields and moduli spaces

TL;DR

This survey explores the moduli spaces of curves over finite fields, focusing on point counting, connections with modular forms, and the stratification of these spaces, highlighting recent developments and open problems.

Contribution

It provides a comprehensive overview of the moduli aspects of curves over finite fields, synthesizing current knowledge and identifying future research directions.

Findings

Counting points of moduli spaces over finite fields

Relations between moduli spaces and modular forms

Stratification structures on moduli spaces

Abstract

This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.