Tohoku Mathematical Journal

On good reduction of some K3 surfaces related to abelian surfaces

Yuya Matsumoto

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 This paper includes T. Ito's unpublished result on Kummer surfaces.

Article information

Source
Tohoku Math. J. (2), Volume 67, Number 1 (2015), 83-104.

Dates
First available in Project Euclid: 20 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1429549580

Digital Object Identifier
doi:10.2748/tmj/1429549580

Mathematical Reviews number (MathSciNet)
MR3337964

Zentralblatt MATH identifier
1361.14027

Subjects
Primary: 11G25: Varieties over finite and local fields [See also 14G15, 14G20]
Secondary: 14G20: Local ground fields 14J28: $K3$ surfaces and Enriques surfaces

Keywords
Good reduction K3 surfaces Kummer surfaces Shioda--Inose structure

Citation

Matsumoto, Yuya. On good reduction of some K3 surfaces related to abelian surfaces. Tohoku Math. J. (2) 67 (2015), no. 1, 83--104. doi:10.2748/tmj/1429549580. https://projecteuclid.org/euclid.tmj/1429549580


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