A Néron–Ogg–Shafarevich criterion for K3 surfaces

Bruno Chiarellotto, Christopher Lazda, Christian Liedtke

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish
Pages (from-to)469-514
Number of pages46
JournalProceedings of the London Mathematical Society
Issue number5
StatePublished - 2019


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


Dive into the research topics of 'A Néron–Ogg–Shafarevich criterion for K3 surfaces'. Together they form a unique fingerprint.

Cite this