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. 73–92DOI 10.4171/RSMUP/50