A monodromy criterion for the good reduction of $K3$ surfaces

Abstract

We give a criterion for the good reduction of semistable K3 surfaces over p-adic fields. We use neither p-adic Hodge theory nor transcendental methods as in the analogous proofs of criteria for good reduction of curves or K3 surfaces. We achieve our goal by realizing the special fiber Xs of a semistable model X of a K3 surface over the p-adic field K, as a special fiber of a log-family in characteristic p and use an arithmetic version of the Clemens-Schmid exact sequence in order to obtain a Kulikov-Persson-Pinkham classification theorem in characteristic p. Mathematics Subject Classification (2010). 14F30, 11G25, 14F35