Good reduction criterion for K3 surfaces

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• 作者：Yuya Matsumoto
• 关键词：K3 surfaces ; Good reduction ; Galois representations ; Period map ; Complex multiplication ; 14J28 ; 11G25 ; 14G20
• 刊名：Mathematische Zeitschrift
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：279
• 期：1-2
• 页码：241-266
• 全文大小：357 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823

文摘

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.