On good reduction of some K3 surfaces related to abelian surfaces

The Neron--Ogg--Safarevic criterion for abelian varieties tells that whether an abelian variety has good reduction or not can be determined from the Galois action on its l-adic etale cohomology. We prove an analogue of this criterion for some special kind of K3 surfaces (those which admit Shioda--Inose structures of product type), which are deeply related to abelian surfaces. We also prove a p-adic analogue. This paper includes Ito's unpublished result for Kummer surfaces.