Abstract
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 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 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.
