Holmstrom Mordell-Lang conjecture

arXiv:1103.2625 On some questions raised by Anand Pillay and Franck Benoist from arXiv Front: math.AG by Damian Rössler We prove that indefinitely $p$-divisible points on abelian varieties defined over function fields of transcendance 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 indefinitely $p$-divisible points of order a power of $p$. Finally, we prove a general result on the sparsity of points in a special fibre of an abelian variety as above, which lift to highly $p$-divisible unramified points; we show how it can be used to give a new proof of the Mordell-Lang conjecture for ordinary abelian varieties.

nLab page on Mordell-Lang conjecture