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

Rössler, Damian

doi:10.2140/ant.2020.14.1123

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

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

Damian Rössler

Vol. 14 (2020), No. 5, 1123–1173

DOI: 10.2140/ant.2020.14.1123

Abstract

Let $A$ be an abelian variety over the function field $K$ of a curve over a finite field. We describe several mild geometric conditions ensuring that the group $A (K^{perf})$ is finitely generated and that the $p$ -primary torsion subgroup of $A (K^{sep})$ is finite. This gives partial answers to questions of Scanlon, Ghioca and Moosa, and Poonen and Voloch. We also describe a simple theory (used to prove our results) relating the Harder–Narasimhan filtration of vector bundles to the structure of finite flat group schemes of height one over projective curves over perfect fields. Finally, we use our results to give a complete proof of a conjecture of Esnault and Langer on Verschiebung divisibility of points in abelian varieties over function fields.

Keywords

abelian varieties, rational points, purely inseparable extensions, Frobenius, Verschiebung

Mathematical Subject Classification 2010

Primary: 11J95

Secondary: 11G10, 14G25

Milestones

Received: 20 September 2018

Revised: 19 November 2019

Accepted: 17 December 2019

Published: 13 July 2020

Authors

Damian Rössler
Mathematical Institute University of Oxford Oxford United Kingdom

Vol. 14, No. 5, 2020