Equidistribution for quasi-projective varieties over function fields

Abstract

We prove equidistribution of small points and subvarieties on quasi-projective varieties over function fields, confirming \cite[Conjecture~5.4.1]{yuan2021adelic} for compactified relatively nef metrized line bundles in the function field case. The argument relies on the generic curves to reduce higher-dimensional bases to curves. We also establish the equidistribution theorem for arithmetically big line bundles using positive intersection.