Work

Degree and height estimates for modular equations on PEL Shimura varieties

Year: 2022

Type: article

Abstract: We define modular equations in the setting of Shimura varieties of PEL type 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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12540

Author: Jean Kieffer

Institution: Harvard University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Cryptography, Isogenies and Abelian varieties Overwhelming