Vol. 14, No. 5, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
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
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(Kperf) is finitely generated and that the p-primary torsion subgroup of A(Ksep) 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