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- Title
Good reduction criterion for K3 surfaces.
- Authors
Matsumoto, Yuya
- Abstract
We prove a Néron-Ogg-Shafarevich type criterion for good reduction of K3 surfaces, which states that a K3 surface over a complete discrete valuation field has potential good reduction if its $$l$$ -adic cohomology group is unramified. We also prove a $$p$$ -adic version of the criterion. (These are analogues of the criteria for good reduction of abelian varieties.) The model of the surface will be in general not a scheme but an algebraic space. As a corollary of the criterion we obtain the surjectivity of the period map of K3 surfaces in positive characteristic.
- Publication
Mathematische Zeitschrift, 2015, Vol 279, Issue 1/2, p241
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-014-1365-8