Quantitativity on the number of rational points in the Mordell conjecture

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Authors: Jiawei Yu, Xinyi Yuan, Shengxuan Zhou
DOI: 10.48550/arxiv.2602.01820
Cited by: 0

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 Kühne. The main body of this paper consists of two parts: Part I for arithmetic estimates and Part II for analytic estimates.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Analytic Number Theory Research Advanced Algebra and Geometry

Publication details

Journal / source
HAL
Publication date
2 February 2026
Language
EN
Document type
Preprint