Galois theory, discriminants and torsion subgroup of elliptic curves

We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve

Detalles Bibliográficos
Autores: García-Selfa, Irene, González Jiménez, Enrique, Tornero, José M.
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:10486/711120
Acceso en línea:http://hdl.handle.net/10486/711120
https://dx.doi.org/10.1016/j.jpaa.2009.11.001
Access Level:acceso abierto
Palabra clave:Galois Representations
Elliptic Curve
P-Adic L-Function
Matemáticas
id ES_e4e061d68ff487792f310f8bdc9c4ebf
oai_identifier_str oai:repositorio.uam.es:10486/711120
network_acronym_str ES
network_name_str España
repository_id_str
spelling Galois theory, discriminants and torsion subgroup of elliptic curvesGarcía-Selfa, IreneGonzález Jiménez, EnriqueTornero, José M.Galois RepresentationsElliptic CurveP-Adic L-FunctionMatemáticasWe find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curveWe would like to thank to F. Beukers, H. Cohen, H. Darmon, L. Dieulefait, J. González and J. Fernández for their useful comments during the preparation of this paper. Special thanks are due to F. Beukers for suggesting the complete parametrization of the Diophantine equation x 2 + 3y 2 = 4z 3 . The first and third authors were supported partially by FQM–218 and P08–FQM–03894 (Junta de Andalucía) and MTM 2007-66929 (Ministerio de Educación y Ciencia, Spain). The research of the second author was supported in part by grants MTM 2009-07291 (Ministerio de Educación y Ciencia, Spain) and CCG09–UAM/ESP–3906 (Universidad Autónoma de Madrid – Comunidad de Madrid, Spain)ElsevierDepartamento de MatemáticasFacultad de Ciencias20102010-08-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/711120https://dx.doi.org/10.1016/j.jpaa.2009.11.001reponame: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:10486/7111202026-06-23T12:46:27Z
dc.title.none.fl_str_mv Galois theory, discriminants and torsion subgroup of elliptic curves
title Galois theory, discriminants and torsion subgroup of elliptic curves
spellingShingle Galois theory, discriminants and torsion subgroup of elliptic curves
García-Selfa, Irene
Galois Representations
Elliptic Curve
P-Adic L-Function
Matemáticas
title_short Galois theory, discriminants and torsion subgroup of elliptic curves
title_full Galois theory, discriminants and torsion subgroup of elliptic curves
title_fullStr Galois theory, discriminants and torsion subgroup of elliptic curves
title_full_unstemmed Galois theory, discriminants and torsion subgroup of elliptic curves
title_sort Galois theory, discriminants and torsion subgroup of elliptic curves
dc.creator.none.fl_str_mv García-Selfa, Irene
González Jiménez, Enrique
Tornero, José M.
author García-Selfa, Irene
author_facet García-Selfa, Irene
González Jiménez, Enrique
Tornero, José M.
author_role author
author2 González Jiménez, Enrique
Tornero, José M.
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Galois Representations
Elliptic Curve
P-Adic L-Function
Matemáticas
topic Galois Representations
Elliptic Curve
P-Adic L-Function
Matemáticas
description We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-08-01
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/10486/711120
https://dx.doi.org/10.1016/j.jpaa.2009.11.001
url http://hdl.handle.net/10486/711120
https://dx.doi.org/10.1016/j.jpaa.2009.11.001
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
repository.mail.fl_str_mv
_version_ 1869422630177603584
score 15.300719

Similares en LA Referencia