On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic II

Damian Rössler

Published 2017-02-23Version 1

Let $A$ be an abelian variety over the function field $K$ of a curve over a finite field. We provide several conditions ensuring that $A(K^{\rm perf})$ is finitely generated. This gives partial answers to questions of Scanlon and Ziegler on the one hand and Esnault and Langer on the other. We also describe the basics of a theory (used to prove our results) relating the Harder-Narasimhan filtration of vector bundles and the structure of finite flat group schemes over projective curves over finite fields.