Infinitely $p$ -Divisible Points on Abelian Varieties Defined over Function Fields of Characteristic $p\gt 0$

Author: 

Rössler, D

Publication Date: 

2013

Journal: 

Notre Dame Journal of Formal Logic

Last Updated: 

2020-01-21T09:11:33.69+00:00

Issue: 

3-4

Volume: 

54

DOI: 

10.1215/00294527-2143943

page: 

579-589

abstract: 

In this article we consider some questions raised by F. Benoist, E. Bouscaren
and A. Pillay. We prove that infinitely $p$-divisible points on abelian
varieties defined over function fields of transcendence degree one over a
finite field are necessarily torsion points. We also prove that when the
endomorphism ring of the abelian variety is $\mZ$ then there are no infinitely
$p$-divisible points of order a power of $p$.

Symplectic id: 

745027

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article