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Good reduction criterion for K3 surfaces: an announcement. (Japanese. English summary) Zbl 1353.14047
Summary: This is an announcement of another paper by the author [Math. Z. 279, No. 1–2, 241–266 (2015; Zbl 1317.14089)]. We prove that whether a K3 surface has potential good reduction can be determined from the Galois representation defined from the $$l$$-adic or $$p$$-adic étale cohomology groups of the K3 surface. This is an analogue of the Neron-Ogg-Shafarevich criterion for Abelian varieties. We also have an application to the period map of K3 surfaces in mixed characteristics.
MSC:
 14J28 $$K3$$ surfaces and Enriques surfaces 11G25 Varieties over finite and local fields 14G20 Local ground fields in algebraic geometry