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For a K3 surface of finite height over a field of odd characteristic, thereexists a smooth lifting to the ring of Witt vectors such that the reduction mapfrom the Picard group of the generic fiber to the Picard group of the specialfiber is isomorphic. In this paper, using this result, we give a criterion fora K3 surface of finite height over a field of odd characteristic to be anEnriques K3 surface or to be a K3 surface in terms of the Neron-Severi lattice.Then we show every Kummer surface has an Enriques involution. We also give aclassification of K3 surfaces of Picard rank of 20 over odd characteristic.

Neron-Severi group preserving lifting of K3 surfaces and applications