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.
Originalsprache | Englisch |
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Seiten (von - bis) | 469-514 |
Seitenumfang | 46 |
Fachzeitschrift | Proceedings of the London Mathematical Society |
Jahrgang | 119 |
Ausgabenummer | 5 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2019 |