zbMATH — the first resource for mathematics

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.
14J28 \(K3\) surfaces and Enriques surfaces
11G25 Varieties over finite and local fields
14G20 Local ground fields in algebraic geometry
PDF BibTeX Cite