Extending Elliptic Curve Chabauty to higher genus curves

TL;DR

This paper generalizes the Elliptic Curve Chabauty method to higher genus curves, enhancing the ability to determine rational points on complex algebraic curves by combining it with covering techniques and a modified Mordell-Weil sieve.

Contribution

It introduces a new approach extending Elliptic Curve Chabauty to higher genus curves, enabling more comprehensive rational point computations.

Findings

Successfully applied to certain higher genus curves

Complements existing methods with combined techniques

Potential to solve previously intractable rational point problems

Abstract

We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to provide a complete solution to the problem of determining the set of rational points of an algebraic curve $Y$.