Abstract
We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors over Jacobians of curves over$\mathbb {Q}$and$\mathbb {F}_q(t)$, and conclude with a pair of hyperkähler 4-folds over$\mathbb {Q}$. The latter is independently interesting as a new example of a transcendental Brauer–Manin obstruction to the Hasse principle. The source code for the various computations is supplied as supplementary material with the online version of this article.
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