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Title: | On a local-global principle for quadratic twists of abelian varieties |
Author: | Fité Naya, Francesc |
Keywords: | Varietats abelianes Geometria algebraica aritmètica Abelian varieties Arithmetical algebraic geometry |
Issue Date: | 6-Dec-2022 |
Publisher: | Springer Verlag |
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 $g=4$. |
Note: | Reproducció del document publicat a: https://doi.org/10.1007/s00208-022-02535-0 |
It is part of: | Mathematische Annalen, 2022, vol. 388, p. 769-794 |
URI: | http://hdl.handle.net/2445/214506 |
Related resource: | https://doi.org/10.1007/s00208-022-02535-0 |
ISSN: | 0025-5831 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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