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arXiv · 1401.1261

Good reduction criterion for K3 surfaces

Yuya Matsumoto
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Abstract

We prove a Neron--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.

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Yuya Matsumoto. 2017-01-05. Good reduction criterion for K3 surfaces. https://doi.org/10.1007/s00209-014-1365-8

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