Rational points on curves over function fields

TL;DR

This paper establishes an upper bound on the number of rational points on algebraic curves over function fields, depending solely on the curve and the base field, independent of the Jacobian.

Contribution

It introduces a new upper bound for rational points on curves over function fields that does not rely on the Jacobian variety.

Findings

Derived an explicit upper bound for rational points

Bound depends only on the curve and the base field

Independent of the Jacobian variety

Abstract

We provide in this paper an upper bound for the number of rational points on a curve defined over a one variable function field over a finite field. The bound only depends on the curve and the field, but not on the Jacobian variety of the curve.