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http://hdl.handle.net/2445/193621
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DC Field | Value | Language |
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dc.contributor.author | Fité Naya, Francesc | - |
dc.contributor.author | Guitart Morales, Xavier | - |
dc.date.accessioned | 2023-02-14T16:10:56Z | - |
dc.date.available | 2023-02-14T16:10:56Z | - |
dc.date.issued | 2020-07-30 | - |
dc.identifier.issn | 1937-0652 | - |
dc.identifier.uri | http://hdl.handle.net/2445/193621 | - |
dc.description.abstract | We determine the set of geometric endomorphism algebras of geometrically split abelian surfaces defined over $\mathbb{Q}$. In particular we find that this set has cardinality 92 . The essential part of the classification consists in determining the set of quadratic imaginary fields $M$ with class group $\mathrm{C}_2 \times \mathrm{C}_2$ for which there exists an abelian surface $A$ defined over $\mathbb{Q}$ which is geometrically isogenous to the square of an elliptic curve with CM by $M$. We first study the interplay between the field of definition of the geometric endomorphisms of $A$ and the field $M$. This reduces the problem to the situation in which $E$ is a $\mathbb{Q}$ curve in the sense of Gross. We can then conclude our analysis by employing Nakamura's method to compute the endomorphism algebra of the restriction of scalars of a Gross $\mathbb{Q}$-curve. | - |
dc.format.extent | 23 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Mathematical Sciences Publishers | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.2140/ant.2020.14.1399 | - |
dc.relation.ispartof | Algebra & Number Theory, 2020, vol. 14, num. 6, p. 1399-1421 | - |
dc.relation.uri | https://doi.org/10.2140/ant.2020.14.1399 | - |
dc.rights | (c) Fité Naya, Francesc et al., 2020 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Teoria de nombres | - |
dc.subject.classification | Varietats de Shimura | - |
dc.subject.classification | Varietats abelianes | - |
dc.subject.classification | Geometria algebraica | - |
dc.subject.other | Number theory | - |
dc.subject.other | Shimura varieties | - |
dc.subject.other | Abelian varieties | - |
dc.subject.other | Algebraic geometry | - |
dc.title | Endomorphism algebras of geometrically split abelian surfaces over $Q$ | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 708392 | - |
dc.date.updated | 2023-02-14T16:10:56Z | - |
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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708392.pdf | 1.36 MB | Adobe PDF | View/Open |
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