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

Cite this article

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

DOI 10.4171/RSMUP/50