Mathematics > Number Theory
[Submitted on 12 Oct 2025
]
Title: Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction
Title: 动机在具有半稳定约化的同源类中的高度有限性
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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