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arXiv · 2601.19757

Integral torsion points on abelian varieties over function fields

Robin de Jong·Nicole Looper·Farbod Shokrieh
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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.

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Robin de Jong, Nicole Looper, Farbod Shokrieh. 2026-01-27. Integral torsion points on abelian varieties over function fields. https://arxiv.org/abs/2601.19757

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