✦ LIBER ✦
Determination of All Q-Rational CM-Points in the Moduli Space of Principally Polarized Abelian Surfaces
✍ Scribed by Naoki Murabayashi; Atsuki Umegaki
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 77 KB
- Volume
- 235
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
It is known that in the moduli space A A of elliptic curves, there exist precisely 9 1 -ޑrational 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 A of principally 2 polarized abelian surfaces, there exist precisely 19 -ޑrational 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.