A classification of Q-curves with complex multiplication

被引：5

作者：

Nakamura, T ^{[1
]}

机构：

[1] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2004年 / 56卷 / 02期

关键词：

Q-curve; elliptic curve; complex multiplication; embedding problem; restriction of scalars;

D O I：

10.2969/jmsj/1191418649

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be the Hilbert class field of an imaginary quadratic field K. An elliptic curve E over H with complex multiplication by K is called a Q-curve if E is isogenous over H to all its Galois conjugates. We classify Q-curves over H, relating them with the cohomology group H-2(H/Q +/- 1). The structures of the abelian varieties over Q obtained from Q-curves by restriction of scalars are investigated.

引用

页码：635 / 648

页数：14

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