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 classi...

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Autores: Dieulefait, L. V. (Luis Victor), Gonzalez-Jimenez, Enrique, Jimenez Urroz, Jorge
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/96600
Acceso en línea:https://hdl.handle.net/2445/96600
Access Level:acceso abierto
Palabra clave:Corbes el·líptiques
Teoria de Galois
Geometria algebraica aritmètica
Grups discontinus
Elliptic curves
Galois theory
Arithmetical algebraic geometry
Discontinuous groups
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spelling On fields of definition of torsion points of elliptic curves with complex multiplicationDieulefait, L. V. (Luis Victor)Gonzalez-Jimenez, EnriqueJimenez Urroz, JorgeCorbes el·líptiquesTeoria de GaloisGeometria algebraica aritmèticaGrups discontinusElliptic curvesGalois theoryArithmetical algebraic geometryDiscontinuous groupsFor 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.American Mathematical Society (AMS)2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/96600Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9939-2010-10621-4Proceedings of the American Mathematical Society, 2011, vol. 139, num. 6, p. 1961-1969http://dx.doi.org/10.1090/S0002-9939-2010-10621-4(c) American Mathematical Society (AMS), 2011info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/966002026-05-27T06:46:51Z
dc.title.none.fl_str_mv On fields of definition of torsion points of elliptic curves with complex multiplication
title On fields of definition of torsion points of elliptic curves with complex multiplication
spellingShingle On fields of definition of torsion points of elliptic curves with complex multiplication
Dieulefait, L. V. (Luis Victor)
Corbes el·líptiques
Teoria de Galois
Geometria algebraica aritmètica
Grups discontinus
Elliptic curves
Galois theory
Arithmetical algebraic geometry
Discontinuous groups
title_short On fields of definition of torsion points of elliptic curves with complex multiplication
title_full On fields of definition of torsion points of elliptic curves with complex multiplication
title_fullStr On fields of definition of torsion points of elliptic curves with complex multiplication
title_full_unstemmed On fields of definition of torsion points of elliptic curves with complex multiplication
title_sort On fields of definition of torsion points of elliptic curves with complex multiplication
dc.creator.none.fl_str_mv Dieulefait, L. V. (Luis Victor)
Gonzalez-Jimenez, Enrique
Jimenez Urroz, Jorge
author Dieulefait, L. V. (Luis Victor)
author_facet Dieulefait, L. V. (Luis Victor)
Gonzalez-Jimenez, Enrique
Jimenez Urroz, Jorge
author_role author
author2 Gonzalez-Jimenez, Enrique
Jimenez Urroz, Jorge
author2_role author
author
dc.subject.none.fl_str_mv Corbes el·líptiques
Teoria de Galois
Geometria algebraica aritmètica
Grups discontinus
Elliptic curves
Galois theory
Arithmetical algebraic geometry
Discontinuous groups
topic Corbes el·líptiques
Teoria de Galois
Geometria algebraica aritmètica
Grups discontinus
Elliptic curves
Galois theory
Arithmetical algebraic geometry
Discontinuous groups
description 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.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/96600
url https://hdl.handle.net/2445/96600
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9939-2010-10621-4
Proceedings of the American Mathematical Society, 2011, vol. 139, num. 6, p. 1961-1969
http://dx.doi.org/10.1090/S0002-9939-2010-10621-4
dc.rights.none.fl_str_mv (c) American Mathematical Society (AMS), 2011
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Mathematical Society (AMS), 2011
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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