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On good reduction of some \(K3\) surfaces (announcement). (Japanese. English summary) Zbl 1362.14037
Summary: This is an abstract of my talk at RIMS conference on 2011/12/02. The full version of the paper is available at arXiv:1202.2421.
The Néron-Ogg-Shafarevich criterion for abelian varieties tells that whether an abelian variety has good reduction or not can be determined from the Galois action on its \(\ell\)-adic étale cohomology. We show an analogue of this criterion for some special kind of K3 surfaces (those which admit Shioda-Inose structures of product type), which are deeply related to abelian surfaces. We also show a \(p\)-adic analogue.
See the final version in [Math. Z. 279, No. 1–2, 241–266 (2015; Zbl 1317.14089)] and the author’s paper in [Tohoku Math. J. (2) 67, No. 1, 83–104 (2015; Zbl 1361.14027)].
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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