Complete classification of the torsion structures of rational elliptic curves over quintic number fields

We classify the possible torsion structures of rational elliptic curves over quintic number fields. In addition, let E be an elliptic curve defined over Q and let G=E(Q)tors be the associated torsion subgroup. We study, for a given G, which possible groups G⊆H could appear such that H=E(K)tors, for...

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Detalles Bibliográficos
Autor: González Jiménez, Enrique
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/711098
Acceso en línea:http://hdl.handle.net/10486/711098
https://dx.doi.org/10.1016/j.jalgebra.2017.01.012
Access Level:acceso abierto
Palabra clave:Rationals
Elliptic Curves
Quintic Number Fields
Torsion Subgroup
Matemáticas
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spelling Complete classification of the torsion structures of rational elliptic curves over quintic number fieldsGonzález Jiménez, EnriqueRationalsElliptic CurvesQuintic Number FieldsTorsion SubgroupMatemáticasWe classify the possible torsion structures of rational elliptic curves over quintic number fields. In addition, let E be an elliptic curve defined over Q and let G=E(Q)tors be the associated torsion subgroup. We study, for a given G, which possible groups G⊆H could appear such that H=E(K)tors, for [K:Q]=5. In particular, we prove that at most there is one quintic number field K such that the torsion grows in the extension K/Q, i.e., E(Q)tors⊊E(K)torsThe author was partially supported by the grant MTM2015-68524-PElsevierDepartamento de MatemáticasFacultad de Ciencias20172017-02-15research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/711098https://dx.doi.org/10.1016/j.jalgebra.2017.01.012reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7110982026-06-23T12:46:27Z
dc.title.none.fl_str_mv Complete classification of the torsion structures of rational elliptic curves over quintic number fields
title Complete classification of the torsion structures of rational elliptic curves over quintic number fields
spellingShingle Complete classification of the torsion structures of rational elliptic curves over quintic number fields
González Jiménez, Enrique
Rationals
Elliptic Curves
Quintic Number Fields
Torsion Subgroup
Matemáticas
title_short Complete classification of the torsion structures of rational elliptic curves over quintic number fields
title_full Complete classification of the torsion structures of rational elliptic curves over quintic number fields
title_fullStr Complete classification of the torsion structures of rational elliptic curves over quintic number fields
title_full_unstemmed Complete classification of the torsion structures of rational elliptic curves over quintic number fields
title_sort Complete classification of the torsion structures of rational elliptic curves over quintic number fields
dc.creator.none.fl_str_mv González Jiménez, Enrique
author González Jiménez, Enrique
author_facet González Jiménez, Enrique
author_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Rationals
Elliptic Curves
Quintic Number Fields
Torsion Subgroup
Matemáticas
topic Rationals
Elliptic Curves
Quintic Number Fields
Torsion Subgroup
Matemáticas
description We classify the possible torsion structures of rational elliptic curves over quintic number fields. In addition, let E be an elliptic curve defined over Q and let G=E(Q)tors be the associated torsion subgroup. We study, for a given G, which possible groups G⊆H could appear such that H=E(K)tors, for [K:Q]=5. In particular, we prove that at most there is one quintic number field K such that the torsion grows in the extension K/Q, i.e., E(Q)tors⊊E(K)tors
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-02-15
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/711098
https://dx.doi.org/10.1016/j.jalgebra.2017.01.012
url http://hdl.handle.net/10486/711098
https://dx.doi.org/10.1016/j.jalgebra.2017.01.012
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
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