Modular abelian varieties over number fields

The main result of this paper is a characterization of the abelian varieties $B / K$ defined over Galois number fields with the property that the $L$-function $L(B / K ; s)$ is a product of $L$-functions of non-CM newforms over $\mathbb{Q}$ for congruence subgroups of the form $\Gamma_1(N)$. The cha...

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Detalles Bibliográficos
Autores: Guitart Morales, Xavier, Quer Bosor, Jordi
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/208182
Acceso en línea:https://hdl.handle.net/2445/208182
Access Level:acceso abierto
Palabra clave:Funcions holomorfes
Varietats abelianes
Holomorphic functions
Abelian varieties
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spelling Modular abelian varieties over number fieldsGuitart Morales, XavierQuer Bosor, JordiFuncions holomorfesVarietats abelianesHolomorphic functionsAbelian varietiesThe main result of this paper is a characterization of the abelian varieties $B / K$ defined over Galois number fields with the property that the $L$-function $L(B / K ; s)$ is a product of $L$-functions of non-CM newforms over $\mathbb{Q}$ for congruence subgroups of the form $\Gamma_1(N)$. The characterization involves the structure of $\operatorname{End}(B)$, isogenies between the Galois conjugates of $B$, and a Galois cohomology class attached to $B / K$. We call the varieties having this property strongly modular. The last section is devoted to the study of a family of abelian surfaces with quaternionic multiplication. As an illustration of the ways in which the general results of the paper can be applied we prove the strong modularity of some particular abelian surfaces belonging to that family, and we show how to find nontrivial examples of strongly modular varieties by twisting.Canadian Mathematical Society.2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/208182Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.4153/CJM-2012-040-2Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 2014, vol. 66, num.1, p. 170-196https://doi.org/10.4153/CJM-2012-040-2cc-by-nc-nd (c) Canadian Mathematical Society., 2014http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2081822026-05-27T06:46:51Z
dc.title.none.fl_str_mv Modular abelian varieties over number fields
title Modular abelian varieties over number fields
spellingShingle Modular abelian varieties over number fields
Guitart Morales, Xavier
Funcions holomorfes
Varietats abelianes
Holomorphic functions
Abelian varieties
title_short Modular abelian varieties over number fields
title_full Modular abelian varieties over number fields
title_fullStr Modular abelian varieties over number fields
title_full_unstemmed Modular abelian varieties over number fields
title_sort Modular abelian varieties over number fields
dc.creator.none.fl_str_mv Guitart Morales, Xavier
Quer Bosor, Jordi
author Guitart Morales, Xavier
author_facet Guitart Morales, Xavier
Quer Bosor, Jordi
author_role author
author2 Quer Bosor, Jordi
author2_role author
dc.subject.none.fl_str_mv Funcions holomorfes
Varietats abelianes
Holomorphic functions
Abelian varieties
topic Funcions holomorfes
Varietats abelianes
Holomorphic functions
Abelian varieties
description The main result of this paper is a characterization of the abelian varieties $B / K$ defined over Galois number fields with the property that the $L$-function $L(B / K ; s)$ is a product of $L$-functions of non-CM newforms over $\mathbb{Q}$ for congruence subgroups of the form $\Gamma_1(N)$. The characterization involves the structure of $\operatorname{End}(B)$, isogenies between the Galois conjugates of $B$, and a Galois cohomology class attached to $B / K$. We call the varieties having this property strongly modular. The last section is devoted to the study of a family of abelian surfaces with quaternionic multiplication. As an illustration of the ways in which the general results of the paper can be applied we prove the strong modularity of some particular abelian surfaces belonging to that family, and we show how to find nontrivial examples of strongly modular varieties by twisting.
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/208182
url https://hdl.handle.net/2445/208182
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.4153/CJM-2012-040-2
Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 2014, vol. 66, num.1, p. 170-196
https://doi.org/10.4153/CJM-2012-040-2
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Canadian Mathematical Society., 2014
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Canadian Mathematical Society., 2014
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Canadian Mathematical Society.
publisher.none.fl_str_mv Canadian Mathematical Society.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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