A parallelogram height inequality for Drinfeld modules

2025/12/10 by Baker, Liam, Griffon, Richard, Pazuki, Fabien
#11G09 #11G50 #14G40 #14K02 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.09526

Abstract

We prove inequalities relating the Taguchi heights, respectively the graded 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 (2025) for abelian varieties over function fields.

Citations

• Variation of height in an isogeny class over a function field
• Isogenies of elliptic curves over function fields
• Explicit Class Field Theory for global function fields

Related

• Heights and isogenies of Drinfeld modules
• Variation of height in an isogeny class over a function field
• Explicit Zsigmondy bounds for families of Drinfeld modules of rank 2
• Heights of Drinfeld modular polynomials and Hecke images
• A lower bound for the canonical height associated to a Drinfeld module