A parallelogram height inequality for Drinfeld modules

Abstract

We prove an inequality relating the Taguchi heights of four Drinfeld modules arranged in a ``parallelogram of isogenies''. This inequality is the analogue for Drinfeld modules of the parallelogram inequality of Rémond (2022) for abelian varieties over number fields and of Griffon--Le Fourn--Pazuki (2026) for abelian varieties over function fields. We also prove a similar inequality for the local graded height at a finite place.

arXiv comment20 pages. V2 improves the exposition and corrects a couple of inaccuracies. Comments are still welcome!