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DC Field | Value | Language |
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dc.contributor.author | Fité Naya, Francesc | - |
dc.date.accessioned | 2024-07-11T06:56:21Z | - |
dc.date.available | 2024-07-11T06:56:21Z | - |
dc.date.issued | 2022-12-06 | - |
dc.identifier.issn | 0025-5831 | - |
dc.identifier.uri | http://hdl.handle.net/2445/214506 | - |
dc.description.abstract | Let $A$ and $A^{\prime}$ be abelian varieties defined over a number field $k$ of dimension $g \geq 1$. For $g \leq 3$, we show that the following local-global principle holds: $A$ and $A^{\prime}$ are quadratic twists of each other if and only if, for almost all primes $\mathfrak{p}$ of $k$ of good reduction for $A$ and $A^{\prime}$, the reductions $A_{\mathfrak{p}}$ and $A_{\mathfrak{p}}^{\prime}$ are quadratic twists of each other. This result is known when $g=1$, in which case it has appeared in works by Kings, Rajan, Ramakrishnan, and Serre. We provide an example that violates this local-global principle in dimension $g=4$. | - |
dc.format.extent | 26 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1007/s00208-022-02535-0 | - |
dc.relation.ispartof | Mathematische Annalen, 2022, vol. 388, p. 769-794 | - |
dc.relation.uri | https://doi.org/10.1007/s00208-022-02535-0 | - |
dc.rights | cc-by (c) Francesc Fité Naya, 2022 | - |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Varietats abelianes | - |
dc.subject.classification | Geometria algebraica aritmètica | - |
dc.subject.other | Abelian varieties | - |
dc.subject.other | Arithmetical algebraic geometry | - |
dc.title | On a local-global principle for quadratic twists of abelian varieties | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 737705 | - |
dc.date.updated | 2024-07-11T06:56:26Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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826694.pdf | 478.51 kB | Adobe PDF | View/Open |
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