“A local-global principle for quadratic twists of abelian varieties”
Mercoledì 23 Aprile 2025, ore 14:30 - Aula 1BC45 - Nirvana Coppola (Università di Padova)
Abstract
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.
