Infinitely $p$-divisible points on abelian varieties defined over function fields of characteristic $p>0$

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 $p$.

References in corpus (3)

• The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields
• Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences
• Around the Mordell-Lang and Manin-Mumford conjectures in positive characteristic

Cited by in corpus (5)

• On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic II
• Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences
• The Brauer-Manin obstruction for nonisotrivial curves over global function fields
• Finiteness and cofiniteness of fine Selmer groups over function fields
• On function field Mordell-Lang: the semiabelian case and the socle theorem