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arXiv · 2512.09526

A parallelogram height inequality for Drinfeld modules

Liam Baker·Richard Griffon·Fabien Pazuki
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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.

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Liam Baker, Richard Griffon, Fabien Pazuki. 2026-09-16. A parallelogram height inequality for Drinfeld modules. https://arxiv.org/abs/2512.09526

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