Q-curves, Hecke characters and some Diophantine equations II

Autores
Pacetti, Ariel Martín; Villagra Torcomian, Lucas
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the article [25] a general procedure to study solutions of the equations x4 − dy2 = zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension Q(√d, √ε)/Q(√d) (where ε is a fundamental unit) needed to prove the existence of a Hecke character over Q(√d) with prescribed local conditions. We also extend some “large image” results due to Ellenberg regarding images of Galois representations coming from Q-curves from imaginary to real quadratic fields.
Fil: Pacetti, Ariel Martín. Universidade de Aveiro; Portugal. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Villagra Torcomian, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
DIOPHANTINE EQUATIONS
Q-CURVES
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:11336/226051
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Q-curves, Hecke characters and some Diophantine equations IIPacetti, Ariel MartínVillagra Torcomian, LucasDIOPHANTINE EQUATIONSQ-CURVEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the article [25] a general procedure to study solutions of the equations x4 − dy2 = zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension Q(√d, √ε)/Q(√d) (where ε is a fundamental unit) needed to prove the existence of a Hecke character over Q(√d) with prescribed local conditions. We also extend some “large image” results due to Ellenberg regarding images of Galois representations coming from Q-curves from imaginary to real quadratic fields.Fil: Pacetti, Ariel Martín. Universidade de Aveiro; Portugal. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Villagra Torcomian, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaUniversitat Autònoma de Barcelona2023-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/226051Pacetti, Ariel Martín; Villagra Torcomian, Lucas; Q-curves, Hecke characters and some Diophantine equations II; Universitat Autònoma de Barcelona; Publicacions Matematiques; 67; 2; 7-2023; 569-5990214-14932014-4350CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.5565/PUBLMAT6722304info:eu-repo/semantics/altIdentifier/url/https://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT6722304info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:29:45Zoai:ri.conicet.gov.ar:11336/226051instacron: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:34982025-10-22 11:29:46.004CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Q-curves, Hecke characters and some Diophantine equations II
title Q-curves, Hecke characters and some Diophantine equations II
spellingShingle Q-curves, Hecke characters and some Diophantine equations II
Pacetti, Ariel Martín
DIOPHANTINE EQUATIONS
Q-CURVES
title_short Q-curves, Hecke characters and some Diophantine equations II
title_full Q-curves, Hecke characters and some Diophantine equations II
title_fullStr Q-curves, Hecke characters and some Diophantine equations II
title_full_unstemmed Q-curves, Hecke characters and some Diophantine equations II
title_sort Q-curves, Hecke characters and some Diophantine equations II
dc.creator.none.fl_str_mv Pacetti, Ariel Martín
Villagra Torcomian, Lucas
author Pacetti, Ariel Martín
author_facet Pacetti, Ariel Martín
Villagra Torcomian, Lucas
author_role author
author2 Villagra Torcomian, Lucas
author2_role author
dc.subject.none.fl_str_mv DIOPHANTINE EQUATIONS
Q-CURVES
topic DIOPHANTINE EQUATIONS
Q-CURVES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the article [25] a general procedure to study solutions of the equations x4 − dy2 = zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension Q(√d, √ε)/Q(√d) (where ε is a fundamental unit) needed to prove the existence of a Hecke character over Q(√d) with prescribed local conditions. We also extend some “large image” results due to Ellenberg regarding images of Galois representations coming from Q-curves from imaginary to real quadratic fields.
Fil: Pacetti, Ariel Martín. Universidade de Aveiro; Portugal. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Villagra Torcomian, Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description In the article [25] a general procedure to study solutions of the equations x4 − dy2 = zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension Q(√d, √ε)/Q(√d) (where ε is a fundamental unit) needed to prove the existence of a Hecke character over Q(√d) with prescribed local conditions. We also extend some “large image” results due to Ellenberg regarding images of Galois representations coming from Q-curves from imaginary to real quadratic fields.
publishDate 2023
dc.date.none.fl_str_mv 2023-07
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/11336/226051
Pacetti, Ariel Martín; Villagra Torcomian, Lucas; Q-curves, Hecke characters and some Diophantine equations II; Universitat Autònoma de Barcelona; Publicacions Matematiques; 67; 2; 7-2023; 569-599
0214-1493
2014-4350
CONICET Digital
CONICET
url http://hdl.handle.net/11336/226051
identifier_str_mv Pacetti, Ariel Martín; Villagra Torcomian, Lucas; Q-curves, Hecke characters and some Diophantine equations II; Universitat Autònoma de Barcelona; Publicacions Matematiques; 67; 2; 7-2023; 569-599
0214-1493
2014-4350
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.5565/PUBLMAT6722304
info:eu-repo/semantics/altIdentifier/url/https://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT6722304
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 Universitat Autònoma de Barcelona
publisher.none.fl_str_mv Universitat Autònoma de Barcelona
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
_version_ 1846781885281206272
score 12.982451

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