论文标题
pel shimura品种模块化方程的程度和高度估计值
Degree and height estimates for modular equations on PEL Shimura varieties
论文作者
论文摘要
我们将模块化方程定义为pel shimura品种的设置为描述Hecke对应关系的方程式，并在其学位和高度上证明了上限。这扩展了有关椭圆模块多项式的已知结果，并意味着使用这些模块化方程的数字理论算法的复杂性界限。特别是，我们获得了针对阿贝尔表面的Siegel和Hilbert类型模块化方程的紧密程度界限。
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.
