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On good reduction of some K3 surfaces related to abelian surfaces. (English) Zbl 1361.14027
Summary: The Néron-Ogg-Shafarevič criterion for abelian varieties tells that the Galois action on the \(\ell\)-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 This paper includes T. Ito’s unpublished result on Kummer surfaces.

MSC:
14J28 \(K3\) surfaces and Enriques surfaces
11G25 Varieties over finite and local fields
14G20 Local ground fields in algebraic geometry
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