|
|||||
 |
|
|
|
|
|
|
|
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 be an abelian variety over the function field of a curve over a finite field. We describe several mild geometric conditions ensuring that the group is finitely generated and that the -primary torsion subgroup of 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. |
PDF Access Denied
We have not been able to recognize your IP address
3.138.125.2
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
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 |
|
