A Torelli theorem for curves over finite fields

TL;DR

This paper explores the relationship between hyperbolic curves and their Jacobians over finite fields within the framework of anabelian geometry, aiming to establish a Torelli-type theorem.

Contribution

It provides a Torelli theorem for hyperbolic curves over finite fields, linking their geometric structure to their Jacobians in anabelian geometry.

Findings

Establishes a Torelli theorem for curves over finite fields

Connects curve isomorphism classes to Jacobian data

Advances understanding of anabelian properties of curves

Abstract

We study hyperbolic curves and their Jacobians over finite fields in the context of anabelian geometry.