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 MordellWeil 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.05235
 Bibcode:
 2021arXiv210805235C
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11G30;
 11D45;
 14G05
 EPrint:
 Accepted Manuscript, to appear in Transactions of the American Mathematical Society. Minor changes in Section 7