Good reduction of K3 surfaces

Compositio mathematica

Yuya Matsumoto^2¹  Christian Liedtke^1² 

[1] Graduate School of Mathematics,Nagoya University,Furocho,Chikusaku,Nagoya, 464-8602,Japan^2;TU München,Zentrum Mathematik - M11,Boltzmannstr. 3,D-85748 Garching bei München,Germany^1

关键词: 14J28;    11G25;    11F80;    14E30 (primary);    K3 surfaces;    good reduction;    Galois representations;   

DOI  :  10.1112/S0010437X17007400

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let $K$ be the field of fractions of a local Henselian discrete valuation ring ${\mathcal{O}}_{K}$ of characteristic zero with perfect residue field $k$. Assuming potential semi-stable reduction, we show that an unramified Galois action on the second $\ell$-adic cohomology group of a K3 surface over $K$ implies that the surface has good reduction after a finite and unramified extension. We give examples where this unramified extension is really needed. Moreover, we give applications to good reduction after tame extensions and Kuga–Satake Abelian varieties. On our way, we settle existence and termination of certain flops in mixed characteristic, and study group actions and their quotients on models of varieties.

【 授权许可】

CC BY