ℚ-curves, Hecke characters and some Diophantine equations II
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/39463 |
Resumo: | In the article [25] a general procedure to study solutions of the equations x^4 − dy^2 = z^p 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( \sqrt{d}, \sqrt{\varepsilon})/Q(\sqrt{d}) (where \varepsilon is a fundamental unit) needed to prove the existence of a Hecke character over Q(\sqrt{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. |
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ℚ-curves, Hecke characters and some Diophantine equations IIQ-curvesDiophantine equationsIn the article [25] a general procedure to study solutions of the equations x^4 − dy^2 = z^p 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( \sqrt{d}, \sqrt{\varepsilon})/Q(\sqrt{d}) (where \varepsilon is a fundamental unit) needed to prove the existence of a Hecke character over Q(\sqrt{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.Universitat Autònoma de Barcelona2023-10-10T09:54:14Z2023-01-01T00:00:00Z2023info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39463eng0214-149310.5565/PUBLMAT6722304Pacetti, ArielTorcomian, Lucas Villagrainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:17:05Zoai:ria.ua.pt:10773/39463Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:09:38.426588Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
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 Q-curves Diophantine equations |
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 |
author |
Pacetti, Ariel |
author_facet |
Pacetti, Ariel Torcomian, Lucas Villagra |
author_role |
author |
author2 |
Torcomian, Lucas Villagra |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Pacetti, Ariel Torcomian, Lucas Villagra |
dc.subject.por.fl_str_mv |
Q-curves Diophantine equations |
topic |
Q-curves Diophantine equations |
description |
In the article [25] a general procedure to study solutions of the equations x^4 − dy^2 = z^p 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( \sqrt{d}, \sqrt{\varepsilon})/Q(\sqrt{d}) (where \varepsilon is a fundamental unit) needed to prove the existence of a Hecke character over Q(\sqrt{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 |
2023-10-10T09:54:14Z 2023-01-01T00:00:00Z 2023 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/39463 |
url |
http://hdl.handle.net/10773/39463 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0214-1493 10.5565/PUBLMAT6722304 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
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:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137747102859264 |