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http://hdl.handle.net/2445/142922
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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 | 2019-10-23T14:54:03Z | - |
dc.date.available | 2019-10-23T14:54:03Z | - |
dc.date.issued | 2018-01-18 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | http://hdl.handle.net/2445/142922 | - |
dc.description.abstract | Let $ A/\mathbb{Q}$ be an abelian variety of dimension $ g\geq 1$ that is isogenous over $ \overline {\mathbb{Q}}$ to $ E^g$, where $ E$ is an elliptic curve. If $ E$ does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition of elliptic $ \mathbb{Q}$-curves, $ E$ is isogenous to a curve defined over a polyquadratic extension of $ \mathbb{Q}$. We show that one can adapt Ribet's methods to study the field of definition of $ E$ up to isogeny also in the CM case. We find two applications of this analysis to the theory of Sato-Tate groups: First, we show that $ 18$ of the $ 34$ possible Sato-Tate groups of abelian surfaces over $ \mathbb{Q}$ occur among at most $ 51$ $ \overline {\mathbb{Q}}$-isogeny classes of abelian surfaces over $ \mathbb{Q}$. Second, we give a positive answer to a question of Serre concerning the existence of a number field over which abelian surfaces can be found realizing each of the $ 52$ possible Sato-Tate groups of abelian surfaces. | - |
dc.format.extent | 37 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/tran/7074 | - |
dc.relation.ispartof | Transactions of the American Mathematical Society, 2018, vol. 370, num. 7, p. 4623-4659 | - |
dc.relation.uri | https://doi.org/10.1090/tran/7074 | - |
dc.rights | cc-by-nc-nd (c) American Mathematical Society (AMS), 2018 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Corbes el·líptiques | - |
dc.subject.classification | Teoria de grups | - |
dc.subject.other | Elliptic curves | - |
dc.subject.other | Group theory | - |
dc.title | Fields of definition of elliptic k-curves and the realizability of all genus 2 Sato-Tate groups of over a number field | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 666561 | - |
dc.date.updated | 2019-10-23T14:54:03Z | - |
dc.relation.projectID | info:eu-repo/grantAgreement/EC/H2020/682152/EU//BSD | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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666561.pdf | 494.66 kB | Adobe PDF | View/Open |
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