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 This paper includes T. Ito's unpublished result on Kummer surfaces.
"On good reduction of some K3 surfaces related to abelian surfaces." Tohoku Math. J. (2) 67 (1) 83 - 104, 2015. https://doi.org/10.2748/tmj/1429549580