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

Rössler, D

2013

Journal:

Notre Dame Journal of Formal Logic

Last Updated:

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

3-4

54

DOI:

10.1215/00294527-2143943

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 $p$.

745027

Not Submitted

Journal Article