Fité Naya, Francesc2024-07-112024-07-112022-12-060025-5831https://hdl.handle.net/2445/214506Let $A$ 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 $g=4$.26 p.application/pdfengcc-by (c) Francesc Fité Naya, 2022http://creativecommons.org/licenses/by/3.0/es/Varietats abelianesGeometria algebraica aritmèticaAbelian varietiesArithmetical algebraic geometryinfo:eu-repo/semantics/article7377052024-07-11info:eu-repo/semantics/openAccess