Degree and height estimates for modular equations on PEL Shimura varieties
KIEFFER, Jean
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
KIEFFER, Jean
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Article de revue
Ce document a été publié dans
Journal of the London Mathematical Society. 2022-03-11, vol. 105, n° 2, p. 1314-1361
London Mathematical Society ; Wiley
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
Hecke correspondences
Shimura varieties
Heights
Abelian varieties
Modular equations
Origine
Importé de halUnités de recherche