# A Néron–Ogg–Shafarevich criterion for K3 surfaces

@article{Chiarellotto2019ANC, title={A N{\'e}ron–Ogg–Shafarevich criterion for K3 surfaces}, author={Bruno Chiarellotto and Christopher Lazda and Christian Liedtke}, journal={Proceedings of the London Mathematical Society}, year={2019} }

The naive analogue of the Néron–Ogg–Shafarevich criterion is false for K3 surfaces, that is, there exist K3 surfaces over Henselian, discretely valued fields K, with unramified l-adic étale cohomology groups, but which do not admit good reduction over K. Assuming potential semi-stable reduction, we show how to correct this by proving that a K3 surface has good reduction if and only if H ét(XK ,Ql) is unramified, and the associated Galois representation over the residue field coincides with the…

## 14 Citations

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We study the good reduction modulo $p$ of $K3$ surfaces with complex multiplication. If a $K3$ surface with complex multiplication has good reduction, we calculate the Picard number and the height…

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Abstract We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over 𝐙{{\mathbf{Z}}}. This gives an analogue for K3 surfaces of Deligne’s…

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We show that for smooth and proper varieties over local fields with no non-trivial vector fields, good reduction descends over purely inseparable extensions. We use this to extend the…

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We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne’s description of the…

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- MathematicsForum of Mathematics, Sigma
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Abstract We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of $K3$ surfaces over finite fields. We prove that every $K3$…

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A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. We give a simple example that an…

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The primary goal of the proposed project was to fully develop the theory of rigid cohomology for local fields in positive characteristic, and to use this to study questions in the arithmetic of…

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- 2020

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The interplay of arithmetic and geometry has had a major impact on the recent development of algebraic geometry and number theory. Over the years, algebraic curves have been a driving force,…

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