Good reduction criterion for K3 surfaces
Algebraic Geometry
2017-01-06 v2 Number Theory
Abstract
We prove a Neron--Ogg--Shafarevich type criterion for good reduction of K3 surfaces, which states that a K3 surface over a complete discrete valuation field has potential good reduction if its -adic cohomology group is unramified. We also prove a -adic version of the criterion. (These are analogues of the criteria for good reduction of abelian varieties.) The model of the surface will be in general not a scheme but an algebraic space. As a corollary of the criterion we obtain the surjectivity of the period map of K3 surfaces in positive characteristic.
Cite
@article{arxiv.1401.1261,
title = {Good reduction criterion for K3 surfaces},
author = {Yuya Matsumoto},
journal= {arXiv preprint arXiv:1401.1261},
year = {2017}
}
Comments
31 Pages, Accepted version (plus minor modifications on Remark 1.2(2), Proposition 2.2(4), Section 5.3, Remark 6.2)