Geometric quadratic Chabauty over number fields

Abstract

This article generalizes the geometric quadratic Chabauty method, initiated over $\mathbb{Q}$ by Edixhoven and Lido, to curves defined over arbitrary number fields. The main result is a conditional bound on the number of rational points on curves that satisfy an additional Chabauty type condition on the Mordell-Weil rank of the Jacobian. The method gives a more direct approach to the generalization by Dogra of the quadratic Chabauty method to arbitrary number fields.

arXiv commentAccepted Manuscript, to appear in Transactions of the American Mathematical Society. Minor changes in Section 7

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• Geometric quadratic Chabauty
• p-adic adelic metrics and Quadratic Chabauty I