On good reduction of some K3 surfaces related to abelian surfaces

Abstract

The Néron--Ogg--Šafarevič criterion for abelian varieties tells that the Galois action on the $l$-adic étale cohomology of an abelian variety over a local field determines whether the variety has good reduction or not. We prove an analogue of this criterion for a certain type of K3 surfaces closely related to abelian surfaces. We also prove its $p$-adic analogue. This paper includes T. Ito's unpublished result on Kummer surfaces.