Proving Modularity for a given elliptic curve over an imaginary quadratic field

Autores
Dieulefait, Luis; Guerberoff, Lucio; Pacetti, Ariel Martín
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH07]) we can associate to an automorphic representation a family of compatible ℓ-adic representations. Our algorithm is based on Faltings-Serre’s method to prove that ℓ-adic Galois representations are isomorphic. Using the algorithm we provide the first examples of modular elliptic curves over imaginary quadratic fields with residual 2-adic image isomorphic to S3 and C3.
Fil: Dieulefait, Luis. Universidad de Barcelona; España
Fil: Guerberoff, Lucio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universite Paris Diderot - Paris 7; Francia
Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Elliptic curves
Modularity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15075
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Proving Modularity for a given elliptic curve over an imaginary quadratic fieldDieulefait, LuisGuerberoff, LucioPacetti, Ariel MartínElliptic curvesModularityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH07]) we can associate to an automorphic representation a family of compatible ℓ-adic representations. Our algorithm is based on Faltings-Serre’s method to prove that ℓ-adic Galois representations are isomorphic. Using the algorithm we provide the first examples of modular elliptic curves over imaginary quadratic fields with residual 2-adic image isomorphic to S3 and C3.Fil: Dieulefait, Luis. Universidad de Barcelona; EspañaFil: Guerberoff, Lucio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universite Paris Diderot - Paris 7; FranciaFil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAmerican Mathematical Society2010-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15075Dieulefait, Luis; Guerberoff, Lucio; Pacetti, Ariel Martín; Proving Modularity for a given elliptic curve over an imaginary quadratic field; American Mathematical Society; Mathematics Of Computation; 79; 270; 4-2010; 1145-11700025-5718enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2010-79-270/S0025-5718-09-02291-1/info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-09-02291-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:44:29Zoai:ri.conicet.gov.ar:11336/15075instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:44:29.49CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Proving Modularity for a given elliptic curve over an imaginary quadratic field
title Proving Modularity for a given elliptic curve over an imaginary quadratic field
spellingShingle Proving Modularity for a given elliptic curve over an imaginary quadratic field
Dieulefait, Luis
Elliptic curves
Modularity
title_short Proving Modularity for a given elliptic curve over an imaginary quadratic field
title_full Proving Modularity for a given elliptic curve over an imaginary quadratic field
title_fullStr Proving Modularity for a given elliptic curve over an imaginary quadratic field
title_full_unstemmed Proving Modularity for a given elliptic curve over an imaginary quadratic field
title_sort Proving Modularity for a given elliptic curve over an imaginary quadratic field
dc.creator.none.fl_str_mv Dieulefait, Luis
Guerberoff, Lucio
Pacetti, Ariel Martín
author Dieulefait, Luis
author_facet Dieulefait, Luis
Guerberoff, Lucio
Pacetti, Ariel Martín
author_role author
author2 Guerberoff, Lucio
Pacetti, Ariel Martín
author2_role author
author
dc.subject.none.fl_str_mv Elliptic curves
Modularity
topic Elliptic curves
Modularity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH07]) we can associate to an automorphic representation a family of compatible ℓ-adic representations. Our algorithm is based on Faltings-Serre’s method to prove that ℓ-adic Galois representations are isomorphic. Using the algorithm we provide the first examples of modular elliptic curves over imaginary quadratic fields with residual 2-adic image isomorphic to S3 and C3.
Fil: Dieulefait, Luis. Universidad de Barcelona; España
Fil: Guerberoff, Lucio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universite Paris Diderot - Paris 7; Francia
Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH07]) we can associate to an automorphic representation a family of compatible ℓ-adic representations. Our algorithm is based on Faltings-Serre’s method to prove that ℓ-adic Galois representations are isomorphic. Using the algorithm we provide the first examples of modular elliptic curves over imaginary quadratic fields with residual 2-adic image isomorphic to S3 and C3.
publishDate 2010
dc.date.none.fl_str_mv 2010-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/15075
Dieulefait, Luis; Guerberoff, Lucio; Pacetti, Ariel Martín; Proving Modularity for a given elliptic curve over an imaginary quadratic field; American Mathematical Society; Mathematics Of Computation; 79; 270; 4-2010; 1145-1170
0025-5718
url http://hdl.handle.net/11336/15075
identifier_str_mv Dieulefait, Luis; Guerberoff, Lucio; Pacetti, Ariel Martín; Proving Modularity for a given elliptic curve over an imaginary quadratic field; American Mathematical Society; Mathematics Of Computation; 79; 270; 4-2010; 1145-1170
0025-5718
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2010-79-270/S0025-5718-09-02291-1/
info:eu-repo/semantics/altIdentifier/doi/10.1090/S0025-5718-09-02291-1
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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