Rational points on twisted K3 surfaces and derived equivalences

Abstract

Using a construction of Hassett--Várilly-Alvarado, we produce derived equivalent twisted K3 surfaces over $\mathbb{Q}$, $\mathbb{Q}_2$, and $\mathbb{R}$, where one has a rational point and the other does not. This answers negatively a question recently raised by Hassett and Tschinkel.

To appear in the proceedings volume for the AIM conference "Brauer groups and obstruction problems: moduli spaces and arithmetic"