Arithmetic of K3 surfaces and derived equivalence

Isogenies of elliptic curves are a fundamental tool in Diophantine geometry. For K3 surfaces, the notion of derived equivalence
plays an analogous role. We review examples where these have been applied to Diophantine problems. By a result of Lieblich-Olsson, two derived equivalent K3 surfaces over a finite field have the same
number of points. We discuss analogous results over local fields.
(joint with Várilly-Alvarado and Tschinkel)