An Explicit Uniform Mordell Conjecture over Function Fields of Characteristic Zero

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.