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Degree and height estimates for modular equations on PEL Shimura varieties

Jean Kieffer 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02436057
Contributor : Jean Kieffer Connect in order to contact the contributor
Submitted on : Monday, August 16, 2021 - 5:57:39 PM
Last modification on : Saturday, December 4, 2021 - 3:43:30 AM

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  • HAL Id : hal-02436057, version 4
  • ARXIV : 2001.04138

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Jean Kieffer. Degree and height estimates for modular equations on PEL Shimura varieties. 2021. ⟨hal-02436057v4⟩

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