Quantitativity on the number of rational points in the Mordell conjecture
Number Theory
2026-02-03 v1 Algebraic Geometry
Differential Geometry
Abstract
In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mordell conjecture proposed by Mazur and proved by Vojta, Dimitrov-Gao-Habegger, and K\"uhne. The main body of this paper consists of two parts: Part I for arithmetic estimates and Part II for analytic estimates.
Cite
@article{arxiv.2602.01820,
title = {Quantitativity on the number of rational points in the Mordell conjecture},
author = {Jiawei Yu and Xinyi Yuan and Shengxuan Zhou},
journal= {arXiv preprint arXiv:2602.01820},
year = {2026}
}