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DC Field | Value | Language |
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dc.contributor.author | Guitart Morales, Xavier | - |
dc.contributor.author | Rotger, Victor | - |
dc.contributor.author | Zhao, Yu | - |
dc.date.accessioned | 2023-03-13T13:39:40Z | - |
dc.date.available | 2023-03-13T13:39:40Z | - |
dc.date.issued | 2014-05 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | https://hdl.handle.net/2445/195115 | - |
dc.description.abstract | Let $F / F_0$ be a quadratic extension of totally real number fields, and let $E$ be an elliptic curve over $F$ which is isogenous to its Galois conjugate over $F_0$. A quadratic extension $M / F$ is said to be almost totally complex (ATC) if all archimedean places of $F$ but one extend to a complex place of $M$. The main goal of this note is to provide a new construction for a supply of Darmon-like points on $E$, which are conjecturally defined over certain ring class fields of $M$. These points are constructed by means of an extension of Darmon's ATR method to higher-dimensional modular abelian varieties, from which they inherit the following features: they are algebraic provided Darmon's conjectures on ATR points hold true, and they are explicitly computable, as we illustrate with a detailed example that provides numerical evidence for the validity of our conjectures. | - |
dc.format.extent | 30 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | American Mathematical Society (AMS) | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1090/S0002-9947-2013-05981-8 | - |
dc.relation.ispartof | Transactions of the American Mathematical Society, 2014, vol. 366, num. 5, p. 2773-2802 | - |
dc.relation.uri | https://doi.org/10.1090/S0002-9947-2013-05981-8 | - |
dc.rights | cc-by-nc-nd (c) American Mathematical Society (AMS), 2014 | - |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Funcions L | - |
dc.subject.classification | Geometria algebraica aritmètica | - |
dc.subject.classification | Teoria de nombres | - |
dc.subject.classification | Corbes el·líptiques | - |
dc.subject.other | L-functions | - |
dc.subject.other | Arithmetical algebraic geometry | - |
dc.subject.other | Number theory | - |
dc.subject.other | Elliptic curves | - |
dc.title | Almost totally complex points on elliptic curves | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 650047 | - |
dc.date.updated | 2023-03-13T13:39:40Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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650047.pdf | 502.54 kB | Adobe PDF | View/Open |
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