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We construct a quasi-canonical lifting of a $K3$ surface of finite heightover a finite field of characteristic $p\geq3$. Such results are previouslyobtained by Nygaard-Ogus when $p\geq5$. For this purpose, we use thedisplay-theoretic deformation theory developed by Langer, Zink, and Lau. Westudy the display structure of the crystalline cohomology of deformations of a$K3$ surface of finite height in terms of the Dieudonn\'e display of theenlarged formal Brauer group.

Construction of quasi-canonical liftings of K3 surfaces of finite height in odd characteristic