Arithmetic bigness and a uniform Bogomolov-type result

• 成果类型: Article
• 署名作者: Yuan, Xinyi
• 署名单位: Peking University
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2026.203.1.2
• 发表日期: 2026-01
• 页码: 15-119
• 关键词: Mordell conjecture; uniform Bogomolov conjecture; adelic line bundle; admissible pairing; admissible canonical bundle; nef adelic line bundles; big adelic line bundles; potentially big; arithmetic intersection number; Arakelov geometry; abelian-varieties; LINE BUNDLES; stable curves; moduli space; conjecture; THEOREM; points; INVARIANTS; families; heights

摘要

In this paper, we construct the admissible canonical bundle of a quasi-projective family of curves, prove that it is a big adelic line bundle when the family has maximal variation, and apply it to prove a uniform Bogomolovtype theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Vojta, Dimitrov-Gao-Habegger and Kuhne. Our treatment is based on the theory of adelic line bundles on quasi-projective varieties recently introduced by Yuan-Zhang.