9 August 2013
Notre Dame Journal of Formal Logic
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 Z, then there are no infinitely p-divisible points of order a power of p.
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