Geometric quadratic Chabauty over number fields

Čoupek, Pavel; Lilienfeldt, David; Xiao, Luciena X.; Yao, Zijian

doi:10.1090/tran/8802

Geometric quadratic Chabauty over number fields
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by Pavel Čoupek, David T.-B. G. Lilienfeldt, Luciena X. Xiao and Zijian Yao HTML | PDF

Trans. Amer. Math. Soc. 376 (2023), 2573-2613 Request permission

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.

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