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We give a criterion for the good reduction of semistable $K3$ surfaces over$p$-adic fields using purely $p$-adic methods. We use neither $p$-adic Hodgetheory nor transcendental methods as in the analogous proofs of criteria forgood reduction of curves or $K3$ surfaces. We achieve our goal by realizing thespecial fiber $X_s$ of a semistable model $X$ of a $K3$ surface over the$p$-adic field $K$, $X_K$ as a special fiber of a log-family in characteristic$p$ and use an arithmetic version of the Clemens-Schimd exact sequence in orderto obtain a Kulikov-Persson-Pinkham classification theorem in characteristic$p$.

Monodromy Criterion for the Good Reduction of K3 Surfaces