Degree and height estimates for modular equations on PEL Shimura varieties

Jean Kieffer

Published 2020-01-13Version 1

We define modular equations in the setting of PEL Shimura varieties as equations describing Hecke correspondences, and prove degree and height bounds for them. This extends known results about classical modular polynomials. In particular, we obtain tight degree bounds for modular equations of Siegel and Hilbert type for abelian surfaces. In the proof, we study the behavior of heights when interpolating rational fractions over number fields; the results we obtain are of independent interest.