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.
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