An Explicit Uniform Mordell Conjecture over Function Fields of Characteristic Zero

TL;DR

This paper proves an explicit uniform version of the Mordell conjecture for non-isotrivial curves over function fields of characteristic zero, utilizing advanced techniques like Vojta's method and Zhang's adelic line bundles.

Contribution

It provides the first explicit uniform bound for the Mordell conjecture in this setting, combining several modern tools and results.

Findings

Established an explicit uniform bound for rational points

Extended the applicability of Vojta's method to function fields

Integrated recent advances in the Bogomolov conjecture proof

Abstract

We give an explicit uniform result on the Mordell conjecture for non-isotrivial curves over function field of characteristic 0. The proof is based on Vojta's method, and make use of Zhang's admissible adelic line bundles and a quantitative proof of the Bogomolov conjecture by Looper-Silverman-Wilms.