Variation of height in an isogeny class over a function field

2025/03/18 by Griffon, Richard, Fourn, Samuel Le, Pazuki, Fabien · 2 citations
#11G10 #11G50 #14G17 #14G25 #14G40 #14K02 #14K15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.14318

Abstract

We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any characteristic). We also prove a parallelogram inequality for abelian varieties in this context, and deduce corollaries of these results.

Cited by

• A parallelogram height inequality for Drinfeld modules
• A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems

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