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# Mathematical Research Letters

## Volume 22 (2015)

### Number 3

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

Pages: 789 – 802

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n3.a9

#### Author

#### Abstract

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.