Good reduction criterion for K3 surfaces

By Yuya Matsumoto. 2014

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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 $$l$$l-adic cohomology group is unramified. We also prove a $$p$$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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f7c198e1fbf1d3358537527f87b268eb73da7b16