A Néron–Ogg–Shafarevich criterion for K3 surfaces

  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},
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… 
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