English

Arithmetic bigness and a uniform Bogomolov-type result

Number Theory 2024-05-01 v4 Algebraic Geometry

Abstract

In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang.

Keywords

Cite

@article{arxiv.2108.05625,
  title  = {Arithmetic bigness and a uniform Bogomolov-type result},
  author = {Xinyi Yuan},
  journal= {arXiv preprint arXiv:2108.05625},
  year   = {2024}
}

Comments

125 pages

R2 v1 2026-06-24T05:03:29.347Z