A monodromy criterion for the good reduction of K3 surfaces
Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 73-92.
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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 X s 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.

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DOI : 10.4171/rsmup/50
Classification : 14, 11
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     author = {Genaro Hernandez-Mada},
     title = {A monodromy criterion for the good reduction of $K3$ surfaces},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {73--92},
     volume = {145},
     year = {2021},
     doi = {10.4171/rsmup/50},
     mrnumber = {4261646},
     zbl = {1465.14040},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/50/}
}
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Genaro Hernandez-Mada. A monodromy criterion for the good reduction of $K3$ surfaces. Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 73-92. doi : 10.4171/rsmup/50. http://www.numdam.org/articles/10.4171/rsmup/50/

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