Variation of height in an isogeny class over a function field
Number Theory
2025-03-19 v1 Algebraic Geometry
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.
Cite
@article{arxiv.2503.14318,
title = {Variation of height in an isogeny class over a function field},
author = {Richard Griffon and Samuel Le Fourn and Fabien Pazuki},
journal= {arXiv preprint arXiv:2503.14318},
year = {2025}
}
Comments
30 pages. Comments are very welcome !