We prove that a K3 surface with an automorphism acting on the global -forms by a primitive -th root of unity, , does not degenerate (assuming the existence of the so-called Kulikov models). A key result used to prove this is the rationality of the actions of automorphisms on the graded quotients of the weight filtration of the -adic cohomology groups of the surface.
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Yuya Matsumoto, Degeneration of K3 surfaces with non-symplectic automorphisms. Rend. Sem. Mat. Univ. Padova (2023),DOI 10.4171/RSMUP/123