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arXiv · 2510.10403

Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction

Alice Lin
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Abstract

Using integral $p$-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.

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Alice Lin. 2025-10-12. Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction. https://arxiv.org/abs/2510.10403

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