On good reduction of some K3 surfaces related to abelian surfaces

Abstract

The Neron--Ogg--Safarevic criterion for abelian varieties tells that whether an abelian variety has good reduction or not can be determined from the Galois action on its l-adic etale cohomology. We prove an analogue of this criterion for some special kind of K3 surfaces (those which admit Shioda--Inose structures of product type), which are deeply related to abelian surfaces. We also prove a p-adic analogue. This paper includes Ito's unpublished result for Kummer surfaces.

arXiv comment21 pages

References in corpus (1)

• Good reduction criterion for K3 surfaces

Cited by in corpus (7)

• Transcendental Brauer groups of products of CM elliptic curves
• Neron-Severi group preserving lifting of K3 surfaces and applications
• The Tate conjecture for K3 surfaces in odd characteristic
• Degeneration of Kummer surfaces
• Reduction of Kummer surfaces modulo 2 in the non-supersingular case
• Explicit desingularisation of Kummer surfaces in characteristic two via specialisation
• Transcendental Brauer-Manin obstructions on singular K3 surfaces