  Arithmetic of K3 surfaces defined over finite fields is investigated. In
particular, we show that any K3 surface of finite height over a finite field k
of characteristic p > 3 has a quasi-canonical lifting to characteristic 0, and
that for any such lifting, the endormorphism algebra of the transcendental
cycles, as a Hodge module, is a CM field. The Tate conjecture for the product
of certain two K3 surfaces is also proved. We illustrate by examples how to
determine explicitly the formal Brauer group associated to a K3 surface over k.
Examples discussed here are all of hypergeometric type.
