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dc.contributor.authorGuitart Morales, Xavier
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.date.accessioned2012-07-09T07:36:39Z
dc.date.created2012
dc.date.issued2012
dc.identifier.citationGuitart, X. Abelian varieties with many endomorphisms and their absolutely simple factors. "Revista matemática iberoamericana", 2012, vol. 28, núm. 2, p. 591-601.
dc.identifier.issn0213-2230
dc.identifier.urihttp://hdl.handle.net/2117/16194
dc.description.abstractWe characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties A/k satisfying that End0 k(A) is a maximal subfield of End0 ¯k (A). We call them Ribet–Pyle varieties over k. We see that every Ribet–Pyle variety over k is isogenous over ¯k to a power of an abelian k-variety and, conversely, that every abelian k-variety occurs as the absolutely simple factor of some Ribet–Pyle variety over k. We deduce from this correspondence a precise description of the absolutely simple factors of the varieties over k of GL2-type.
dc.format.extent11 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
dc.subject.lcshAbelian varieties
dc.subject.lcshArithmetical algebraic geometry.
dc.titleAbelian varieties with many endomorphisms and their absolutely simple factors
dc.typeArticle
dc.subject.lemacVarietats abelianes
dc.subject.lemacEsquemes (Geometria algebraica)
dc.subject.lemacGeometria algebraica aritmètica
dc.contributor.groupUniversitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
dc.identifier.doi10.4171/rmi/686
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
dc.subject.amsClassificació AMS::14 Algebraic geometry::14K Abelian varieties and schemes
dc.relation.publisherversionhttp://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=28&iss=2&rank=8
dc.rights.accessRestricted access - publisher's policy
local.identifier.drac10656016
dc.description.versionPostprint (published version)
dc.date.lift10000-01-01
local.citation.authorGuitart, X.
local.citation.publicationNameRevista matemática iberoamericana
local.citation.volume28
local.citation.number2
local.citation.startingPage591
local.citation.endingPage601


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