A monodromy criterion for the good reduction of 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 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 .
@article{RSMUP_2021__145__73_0,
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/}
}
TY - JOUR AU - Genaro Hernandez-Mada TI - A monodromy criterion for the good reduction of $K3$ surfaces JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2021 SP - 73 EP - 92 VL - 145 UR - http://www.numdam.org/articles/10.4171/rsmup/50/ DO - 10.4171/rsmup/50 LA - en ID - RSMUP_2021__145__73_0 ER -
%0 Journal Article %A Genaro Hernandez-Mada %T A monodromy criterion for the good reduction of $K3$ surfaces %J Rendiconti del Seminario Matematico della Università di Padova %D 2021 %P 73-92 %V 145 %U http://www.numdam.org/articles/10.4171/rsmup/50/ %R 10.4171/rsmup/50 %G en %F RSMUP_2021__145__73_0
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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