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Modular abelian varieties over number fields
dc.contributor.author | Guitart Morales, Xavier |
dc.contributor.author | Quer Bosor, Jordi |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2014-02-03T13:56:12Z |
dc.date.created | 2014 |
dc.date.issued | 2014 |
dc.identifier.citation | Guitart, X.; Quer, J. Modular abelian varieties over number fields. "Canadian journal of mathematics. Journal canadien de mathématiques", 2014, vol. 66, núm. 1, p. 170-196. |
dc.identifier.issn | 0008-414X |
dc.identifier.uri | http://hdl.handle.net/2117/21433 |
dc.description.abstract | 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 Q for congruence subgroups of the form T1(N). The characterization involves the structure of 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. |
dc.format.extent | 27 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica |
dc.subject.lcsh | Abelian varieties |
dc.subject.lcsh | Arithmetical algebraic geometry |
dc.subject.other | Modular abelian varieties |
dc.subject.other | GL2-type varieties |
dc.subject.other | Modular forms |
dc.title | Modular abelian varieties over number fields |
dc.type | Article |
dc.subject.lemac | Varietats abelianes |
dc.subject.lemac | Esquemes (Geometria algebraica) |
dc.subject.lemac | Geometria algebraica aritmètica |
dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
dc.identifier.doi | 10.4153/CJM-2012-040-2 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::14 Algebraic geometry::14K Abelian varieties and schemes |
dc.subject.ams | Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) |
dc.relation.publisherversion | http://cms.math.ca/10.4153/CJM-2012-040-2 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 11053719 |
dc.description.version | Postprint (published version) |
dc.date.lift | 10000-01-01 |
local.citation.author | Guitart, X.; Quer, J. |
local.citation.publicationName | Canadian journal of mathematics. Journal canadien de mathématiques |
local.citation.volume | 66 |
local.citation.number | 1 |
local.citation.startingPage | 170 |
local.citation.endingPage | 196 |
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