  We study the good reduction modulo p of K3 surfaces with complex
multiplication. If a K3 surface with complex multiplication has good reduction,
we calculate the Picard number and the height of the formal Brauer group of the
reduction. Moreover, if the reduction is supersingular, we calculate its Artin
invariant under some assumptions. Our results generalize some results of
Shimada for K3 surfaces with Picard number 20. Our methods rely on the main
theorem of complex multiplication for K3 surfaces by Rizov, an explicit
description of the Breuil-Kisin modules associated with Lubin-Tate characters
due to Andreatta, Goren, Howard, and Madapusi Pera, and the integral comparison
theorem recently established by Bhatt, Morrow, and Scholze.
