Néron-Severi group preserving lifting of $\mathrm{K}3$ surfaces and applications

For complex algebraic $\mathrm{K}3$ surfaces, there are criteria in terms of Néron-Severi lattice to be a Kummer surface and to be an Enriques $\mathrm{K}3$ surface. In this paper, using a Néron-Severi group preserving lifting, we prove that the same criteria hold for $\mathrm{K}3$ surfaces of finite height over a field of odd characteristic. We also classify $\mathrm{K}3$ surfaces of Picard number $20$ over a field of odd characteristic.

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Published 20 May 2015