STNB2025 (38th edition)
A local-global principle for quadratic twists of abelian varieties
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Nirvana Coppola
Resumen
Given two abelian varieties over a number field $K$, we say that they are quadratic twists if they become isogenous after taking a quadratic extension of the base field. We moreover say that they are (strongly) locally quadratic twists if their reduction modulo almost all primes of $K$ (or base-change to almost all completions of $K$) are quadratic twists. Clearly, two abelian varieties that are globally quadratic twists will also be (strongly) locally quadratic twists. The converse is not necessarily true. In this talk I will give an overview of results and counterexamples, based on joint work with E. Ambrosi and F. Fité.
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