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http://hdl.handle.net/2445/193366
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DC Field | Value | Language |
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dc.contributor.author | Guitart Morales, Xavier | - |
dc.date.accessioned | 2023-02-09T17:01:28Z | - |
dc.date.available | 2023-02-09T17:01:28Z | - |
dc.date.issued | 2012 | - |
dc.identifier.issn | 0213-2230 | - |
dc.identifier.uri | http://hdl.handle.net/2445/193366 | - |
dc.description.abstract | We characterize the abelian varieties arising as absolutely simple factors of $\mathrm{GL}_2$-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 $\operatorname{End}_k^0(A)$ is a maximal subfield of $\operatorname{End}_{\bar{k}}^0(A)$. We call them Ribet-Pyle varieties over $k$. We see that every Ribet-Pyle variety over $k$ is isogenous over $\bar{k}$ 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 $\mathrm{GL}_2$-type. | - |
dc.format.extent | 11 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | European Mathematical Society Publishing House | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.4171/rmi/686 | - |
dc.relation.ispartof | Revista Matematica Iberoamericana, 2012, vol. 28, num. 2, p. 591-601 | - |
dc.relation.uri | https://doi.org/10.4171/rmi/686 | - |
dc.rights | (c) European Mathematical Society Publishing House, 2012 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Geometria algebraica | - |
dc.subject.classification | Teoria de nombres | - |
dc.subject.classification | Varietats abelianes | - |
dc.subject.classification | K-teoria | - |
dc.subject.other | Algebraic geometry | - |
dc.subject.other | Number theory | - |
dc.subject.other | Abelian varieties | - |
dc.subject.other | K-theory | - |
dc.title | Abelian varieties with many endomorphisms and their absolutely simple factors | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 650043 | - |
dc.date.updated | 2023-02-09T17:01:28Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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650043.pdf | 190.5 kB | Adobe PDF | View/Open |
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