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arXiv · 1103.2625

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

Damian Rössler
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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 $p$.

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Damian Rössler. 2011-03-14. Infinitely $p$-divisible points on abelian varieties defined over function fields of characteristic $p>0$. https://doi.org/10.1215/00294527-2143943

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