Abelian surfaces admitting an (l, l)-endomorphism

被引：3

作者：

Broeker, Reinier ^{[1
]}

Lauter, Kristin ^{[2
]}

Streng, Marco ^{[3
]}

机构：

[1] Brown Univ, Dept Math, Providence, RI 02912 USA

[2] Microsoft Res, Redmond, WA 98052 USA

[3] Leiden Univ, NL-2300 RA Leiden, Netherlands

来源：

JOURNAL OF ALGEBRA | 2013年 / 394卷

基金：

英国工程与自然科学研究理事会;

关键词：

Abelian surfaces; Isogenies; Modular polynomials and correspondences; Hyperelliptic curves; Hermitian forms; CM points; Humbert surfaces; Shimura curves; Clueing elliptic curves; Complex multiplication; Genus two; GENUS; 2; CURVES;

D O I：

10.1016/j.jalgebra.2013.07.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：374 / 396

页数：23

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