Abelian surfaces admitting an (l, l)-endomorphism

作者：Broeker Reinier; Lauter Kristin; Streng Marco^*

来源：Journal of Algebra, 2013, 394: 374-396.

DOI：10.1016/j.jalgebra.2013.07.011

• Abelian surfaces
• Isogenies
• Modular polynomials and correspondences
• Hyperelliptic curves
• Hermitian forms
• CM points
• Humbert surfaces
• Shimura curves
• Clueing elliptic curves
• Complex multiplication
• Genus two

We give a classification of all principally polarized abelian surfaces that admit an (l, l)-isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case l = 2. As part of our classification, we also show how to find all principally polarized abelian surfaces with multiplication by a given imaginary quadratic order.

• 出版日期2013-11-15
• 单位Microsoft