A geometric linear Chabauty comparison theorem
arXiv:2102.04967
Abstract
The Chabauty-Coleman method is a -adic method for finding all rational points on curves of genus whose Jacobians have Mordell-Weil rank . Recently, Edixhoven and Lido developed a geometric quadratic Chabauty method that was adapted by Spelier to cover the case of geometric linear Chabauty. We compare the geometric linear Chabauty method and the Chabauty-Coleman method and show that geometric linear Chabauty can outperform Chabauty-Coleman in certain cases. However, as Chabauty-Coleman remains more practical for general computations, we discuss how to strengthen Chabauty-Coleman to make it theoretically equivalent to geometric linear Chabauty. We apply these methods to genus 2 and genus 3 curves.
fixed minor issues and updated exposition; to appear in Acta Arithmetica