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arXiv · 2108.05235

Geometric quadratic Chabauty over number fields

Pavel Čoupek·David T. -B. G. Lilienfeldt·Zijian Yao·Luciena Xiao Xiao
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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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Pavel Čoupek, David T. -B. G. Lilienfeldt, Zijian Yao, Luciena Xiao Xiao. 2021-08-11. Geometric quadratic Chabauty over number fields. https://doi.org/10.1090/tran%2F8802

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