Integral torsion points on abelian varieties over function fields

arXiv (Cornell University)

Abstract

We prove an analogue, over global function fields, of a conjecture due to Su-Ion Ih concerning the non-Zariski density of torsion points on abelian varieties that are integral with respect to a given non-special divisor. Along the way, we establish a Tate--Voloch type theorem for abelian varieties over completions of global function fields, which allows us to obtain a logarithmic equidistribution result for Galois orbits of torsion points.

Authors 3

1. Robin de Jong Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   Leiden University , Einsteinweg 55 , 2333 CC Leiden , The Netherlands

2. Nicole Looper
3. Farbod Shokrieh Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   Leiden University , Einsteinweg 55 , 2333 CC Leiden , The Netherlands