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In this paper, we prove that, over an algebraically closed field of oddcharacteristic, a weakly tame automorphism of a K3 surface of finite height canbe lifted over the ring of Witt vectors of the base field. Also we prove that anon-symplectic tame automorphism of a supersingular K3 surface or a symplectictame automorphism of a supersingular K3 surface of Artin-invariant at least 2can be lifted over the ring of Witt vectors. Using these results, we prove, fora weakly tame K3 surface of finite height, there is a lifting over the ring ofWitt vectors to which whole the automorphism group of the K3 surface can belifted. Also we prove a K3 surface equipped with a purely non-symplecticautomorphism of a certain order is unique up to isomorphism.

A lifting of an automorphism of a K3 surface over odd characteristic