Papers › A geometric linear Chabauty comparison theorem
A geometric linear Chabauty comparison theorem
Sachi Hashimoto, Pim Spelier
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The Chabauty-Coleman method is a p-adic method for finding all rational points on curves of genus g whose Jacobians have Mordell-Weil rank r < g. 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.
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