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Tohoku Mathematical Journal
SECOND SERIES VOL. 67, NO. 1
|Tohoku Math. J.|
67 (2015), 83-104
ON GOOD REDUCTION OF SOME K3 SURFACES RELATED TO ABELIAN SURFACES
(Received July 1, 2013, revised January 20, 2014)
The Néron--Ogg--Šafarevič criterion for abelian varieties tells that the Galois action on the $l$-adic étale cohomology of an abelian variety over a local field determines whether the variety has good reduction or not. We prove an analogue of this criterion for a certain type of K3 surfaces closely related to abelian surfaces. We also prove its $p$-adic analogue. This paper includes T. Ito's unpublished result on Kummer surfaces.
Mathematics Subject Classification.
Primary 11G25; Secondary 14G20, 14J28.
Key words and phrases.
Good reduction, K3 surfaces, Kummer surfaces, Shioda--Inose structure.
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