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Abelian varieties with many endomorphisms and their absolutely simple factors
dc.contributor.author | Guitart Morales, Xavier |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2012-07-09T07:36:39Z |
dc.date.created | 2012 |
dc.date.issued | 2012 |
dc.identifier.citation | Guitart, X. Abelian varieties with many endomorphisms and their absolutely simple factors. "Revista matemática iberoamericana", 2012, vol. 28, núm. 2, p. 591-601. |
dc.identifier.issn | 0213-2230 |
dc.identifier.uri | http://hdl.handle.net/2117/16194 |
dc.description.abstract | We 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.extent | 11 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.title | Abelian varieties with many endomorphisms and their absolutely simple factors |
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 | 10.4171/rmi/686 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) |
dc.subject.ams | Classificació AMS::14 Algebraic geometry::14K Abelian varieties and schemes |
dc.relation.publisherversion | http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=28&iss=2&rank=8 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 10656016 |
dc.description.version | Postprint (published version) |
dc.date.lift | 10000-01-01 |
local.citation.author | Guitart, X. |
local.citation.publicationName | Revista matemática iberoamericana |
local.citation.volume | 28 |
local.citation.number | 2 |
local.citation.startingPage | 591 |
local.citation.endingPage | 601 |
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