On fields of definition of torsion points of elliptic curves with complex multiplication

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 ca...

Descripción completa

Detalles Bibliográficos
Autores: Dieulefait, Luis, González Jiménez, Enrique, Urroz, Jorge Jiḿenez
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/711200
Acceso en línea:http://hdl.handle.net/10486/711200
https://dx.doi.org/10.1090/S0002-9939-2010-10621-4
Access Level:acceso abierto
Palabra clave:Torsion
Elliptic Curves
Galois Representation
Matemáticas
Descripción
Sumario: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