On fields of definition of torsion points of elliptic curves with complex multiplication
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- by Luis Dieulefait, Enrique González-Jiménez and Jorge Jiménez Urroz PDF
- Proc. Amer. Math. Soc. 139 (2011), 1961-1969 Request permission
Abstract:
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.References
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Additional Information
- Luis Dieulefait
- Affiliation: Departament d’Algebra i Geometria, Universitat de Barcelona, G. V. de les Corts Catalanes 585, 08007 Barcelona, Spain
- MR Author ID: 671876
- Email: ldieulefait@ub.edu
- Enrique González-Jiménez
- Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain
- MR Author ID: 703386
- Email: enrique.gonzalez.jimenez@uam.es
- Jorge Jiménez Urroz
- Affiliation: Departament de Matemàtica Aplicada IV, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
- Email: jjimenez@ma4.upc.edu
- Received by editor(s): March 16, 2010
- Received by editor(s) in revised form: June 2, 2010
- Published electronically: November 9, 2010
- Additional Notes: The authors were partially supported by the grants MTM2006-04895 (Ministerio de Educación y Ciencia of Spain), MTM2009-07291 (Ministerio de Ciencia e Innovación of Spain), CCG08-UAM/ESP-3906 (Universidad Autónoma de Madrid and Comunidad de Madrid), and MTM2009-11068 (Ministerio de Ciencia e Innovación of Spain) respectively.
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1961-1969
- MSC (2010): Primary 11G05; Secondary 11F80
- DOI: https://doi.org/10.1090/S0002-9939-2010-10621-4
- MathSciNet review: 2775372