Integral torsion points on abelian varieties over function fields
Number Theory
2026-01-28 v1 Algebraic Geometry
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.
Cite
@article{arxiv.2601.19757,
title = {Integral torsion points on abelian varieties over function fields},
author = {Robin de Jong and Nicole Looper and Farbod Shokrieh},
journal= {arXiv preprint arXiv:2601.19757},
year = {2026}
}