Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction
Number Theory
2025-10-14 v1 Algebraic Geometry
Abstract
Using integral -adic Hodge theory, Kato and Koshikawa define a generalization of the Faltings height of an abelian variety to motives defined over a number field. Assuming the adelic Mumford-Tate conjecture, we prove a finiteness property for heights in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field. This expands on a result of Kisin and Mocz for the Faltings height in isogeny classes of abelian varieties.
Keywords
Cite
@article{arxiv.2510.10403,
title = {Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction},
author = {Alice Lin},
journal= {arXiv preprint arXiv:2510.10403},
year = {2025}
}