Open Access
2015 On good reduction of some K3 surfaces related to abelian surfaces
Yuya Matsumoto
Tohoku Math. J. (2) 67(1): 83-104 (2015). DOI: 10.2748/tmj/1429549580


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 This paper includes T. Ito's unpublished result on Kummer surfaces.


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Yuya Matsumoto. "On good reduction of some K3 surfaces related to abelian surfaces." Tohoku Math. J. (2) 67 (1) 83 - 104, 2015.


Published: 2015
First available in Project Euclid: 20 April 2015

zbMATH: 1361.14027
MathSciNet: MR3337964
Digital Object Identifier: 10.2748/tmj/1429549580

Primary: 11G25
Secondary: 14G20 , 14J28

Keywords: good reduction , K3 surfaces , Kummer surfaces , Shioda--Inose structure

Rights: Copyright © 2015 Tohoku University

Vol.67 • No. 1 • 2015
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