A Néron–Ogg–Shafarevich criterion for K3 surfaces

Bruno Chiarellotto, Christopher Lazda, Christian Liedtke

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

7 Zitate (Scopus)

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.

OriginalspracheEnglisch
Seiten (von - bis)469-514
Seitenumfang46
FachzeitschriftProceedings of the London Mathematical Society
Jahrgang119
Ausgabenummer5
DOIs
PublikationsstatusVeröffentlicht - 2019

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