Mon, December 8, 2025
4:00 pm - 5:00 pm
Math Tower (MW) 154
Alice Lin
Harvard University
Title
Finiteness of heights in isogeny classes of motives
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.