Degree and height estimates for modular equations on PEL Shimura varieties
Algebraic Geometry
2022-03-09 v4 Number Theory
Abstract
We define modular equations in the setting of PEL Shimura varieties as equations describing Hecke correspondences, and prove upper bounds on their degrees and heights. This extends known results about elliptic modular polynomials, and implies complexity bounds for number-theoretic algorithms using these modular equations. In particular, we obtain tight degree bounds for modular equations of Siegel and Hilbert type for abelian surfaces.
Cite
@article{arxiv.2001.04138,
title = {Degree and height estimates for modular equations on PEL Shimura varieties},
author = {Jean Kieffer},
journal= {arXiv preprint arXiv:2001.04138},
year = {2022}
}
Comments
Final version to appear in the Journal of the London Mathematical Society