Determination of all Q-rational CM-points in the moduli space of principally polarized abelian surfaces
Determination of all Q-rational CM-points in the moduli space of principally polarized abelian surfaces
复制标题
主极化阿贝尔面模空间中所有 Q 有理 CM 点的确定
DOI：
10.1006/jabr.2000.8453
复制
发表时间：
2001
影响因子：
0.9
通讯作者：
A. Umegaki
中科院分区：
文献类型：
--
作者：
N. Murabayashi;A. Umegaki
摘要已知在椭圆曲线的模空间a1中，有精确的9个Q -有理点对应于主虚二次数域的代数整数环复乘的椭圆曲线同构类。本文证明了在主极化阿贝尔曲面的模空间a2中，精确地存在19个对应于阿贝尔曲面同构类的Q -有理点，这些曲面的自同构环与某些虚循环四次数域的代数整数环同构。
Abstract It is known that in the moduli space A 1 of elliptic curves, there exist precisely 9 Q -rational points corresponding to the isomorphism class of elliptic curves with complex multiplication by the ring of algebraic integers of a principal imaginary quadratic number field. Here, we prove that in the moduli space A 2 of principally polarized abelian surfaces, there exist precisely 19 Q -rational points corresponding to the isomorphism class of abelian surfaces whose endomorphism rings are isomorphic to the rings of algebraic integers of some imaginary cyclic quartic number fields.