ON FIELDS OF DEFINITION OF TORSION POINTS OF ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION

被引：7

作者：

Dieulefait, Luis ^{[1
]}

Gonzalez-Jimenez, Enrique ^{[2
,3
]}

Jimenez Urroz, Jorge ^{[4
]}

机构：

[1] Univ Barcelona, Dept Algebra & Geometria, E-08007 Barcelona, Spain

[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[3] CSIC UAM UC3M UCM, Inst Ciencia Matemat, Madrid 28049, Spain

[4] Univ Politecn Cataluna, Dept Matemat Aplicada 4, ES-08034 Barcelona, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 06期

关键词：

Elliptic curves; torsion; Galois representation; SUBGROUPS;

D O I：

10.1090/S0002-9939-2010-10621-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves; in particular, we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.

引用

页码：1961 / 1969

页数：9

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