Slope boundedness and Equidistribution theorem

Abstract

In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic 0. This can be applied to prove the equidistribution of generic and small points with respect to a big and semipositive adelic line bundle. Our methods can be applied to the finite places of number fields as well. We also show the continuity of $\chi$-volumes over function fields.

References in corpus (2)

• Non-Archimedean volumes of metrized nef line bundles
• A relative bigness inequality and equidistribution theorem over function fields