## Abstract

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 (Formula presented.) is unramified, and the associated Galois representation over the residue field coincides with the second cohomology of a certain ‘canonical reduction’ of X. We also prove the corresponding results for p-adic étale cohomology.

Original language | English |
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Pages (from-to) | 469-514 |

Number of pages | 46 |

Journal | Proceedings of the London Mathematical Society |

Volume | 119 |

Issue number | 5 |

DOIs | |

State | Published - 2019 |

## Keywords

- 11G25
- 14F20
- 14F30
- 14G20 (secondary)
- 14J28 (primary)