Height inequality of algebraic points on curves over functional fields

TL;DR

This paper establishes a linear and effective height inequality for algebraic points on curves over functional fields, linking it to a logarithmic canonical class inequality of punctured curves.

Contribution

It introduces a new height inequality for algebraic points on curves over functional fields, extending the understanding of height bounds in this setting.

Findings

Provides a linear, effective height inequality for algebraic points.

Connects height inequality to logarithmic canonical class inequality.

Enhances tools for studying algebraic points over functional fields.

Abstract

The purpose of this paper is to give a linear and effective height inequality for algebraic points on curves over functional fields. Our height inequality can be viewed as the logarithmic canonical class inequality of a punctured curve over a functional field (a fibered surface minus a section).