Heights on quaternionic Shimura varieties

Abstract: We give an explicit formula for the height of a special point on a quaternionic Shimura variety in terms of Faltings heights of CM abelian varieties. This is a generalization of the work of Yuan and Zhang on proving the averaged Colmez conjecture. We also show an application of this formula to the Andre-Oort conjecture, which was recently proven by Pila, Shankar, and Tsimerman.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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