Tohoku Mathematical Journal
2015
March
SECOND SERIES VOL. 67, NO. 1

Tohoku Math. J.
67 (2015), 83-104

Title ON GOOD REDUCTION OF SOME K3 SURFACES RELATED TO ABELIAN SURFACES

Author Yuya Matsumoto

(Received July 1, 2013, revised January 20, 2014)
Abstract. 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 This paper includes T. Ito's unpublished result on Kummer surfaces.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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