Degeneration of K3 surfaces and automorphisms

We prove that a K3 surface with an automorphism acting on the global 2-forms by a primitive $m$-th root of unity does not degenerate if $m \neq 1,2,3,4,6$ (assuming the existence of the so-called Kulikov models). To prove this we study the rationality of the actions of automorphisms on the graded quotients of the weight filtration of the $l$-adic cohomology groups.Non UBCUnreviewedAuthor affiliation: University of TokyoPostdoctora