Geometric quadratic Chabauty over number fields

Pavel Čoupek, David T. -B. G. Lilienfeldt, Zijian Yao, Luciena Xiao Xiao

Published 2021-08-11Version 1

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.