A monodromy criterion for the good reduction of K3K3 surfaces

  • Genaro Hernandez-Mada

    Universidad de Sonora, Hermosillo, Mexico
A monodromy criterion for the good reduction of $K3$ surfaces cover
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Abstract

We give a criterion for the good reduction of semistable K3K3 surfaces over pp-adic fields. We use neither pp-adic Hodge theory nor transcendental methods as in the analogous proofs of criteria for good reduction of curves or K3K3 surfaces. We achieve our goal by realizing the special fiber XsX_s of a semistable model XX of a K3K3 surface over the pp-adic field KK, as a special fiber of a log-family in characteristic pp and use an arithmetic version of the Clemens–Schmid exact sequence in order to obtain a Kulikov–Persson–Pinkham classification theorem in characteristic pp.

Cite this article

Genaro Hernandez-Mada, A monodromy criterion for the good reduction of K3K3 surfaces. Rend. Sem. Mat. Univ. Padova 145 (2021), pp. 73–92

DOI 10.4171/RSMUP/50