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]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Journal of the London Mathematical Society. 2022-03-11, vol. 105, n° 2, p. 1314-1361
London Mathematical Society ; Wiley
English 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 ...Read more >
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.Read less <
English Keywords
Hecke correspondences
Shimura varieties
Heights
Abelian varieties
Modular equations
Origin
Hal imported