Good reduction criterion for K3 surfaces

被引：21

作者：

Matsumoto, Yuya ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2015年 / 279卷 / 1-2期

关键词：

K3; surfaces; Good reduction; Galois representations; Period map; Complex multiplication; WEIGHT SPECTRAL SEQUENCES; SEMI-STABLE REDUCTION; ABELIAN-VARIETIES; ARTIN STACKS; CRYSTALLINE COHOMOLOGY; 6; OPERATIONS; CURVES; RAMIFICATION; COEFFICIENTS; MODULES;

D O I：

10.1007/s00209-014-1365-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a N,ron-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.

引用

页码：241 / 266

页数：26

共 48 条

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