Submission date: 23 February 2017

Abstract:

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^{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.

Mathematics Subject Classification: 14K05

Keywords and phrases:

Full text arXiv 1702.07142: pdf, ps.