论文标题
积极特征的McKay对应关系
A McKay Correspondence in Positive Characteristic
论文作者
论文摘要
我们为$ \ mathrm {sl} _2 $的有限和还原的亚组方案建立了McKay对应关系。作为一个应用程序，我们获得了特征性$ p \ geq7 $中所有理性双点奇点的McKay对应关系。我们讨论了在Witt矢量环上线性还原的奇异性和规范升降机。在维度2中，我们通过$ g $ -Hilbert Shemes建立了这些规范升降机的奇异性分辨率。在附录中，我们讨论了有限群体方案的共轭类概念的几种方法：这是McKay通信中的一种成分，但也具有独立的兴趣。
We establish a McKay correspondence for finite and linearly reductive subgroup schemes of $\mathrm{SL}_2$ in positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in characteristic $p\geq7$. We discuss linearly reductive quotient singularities and canonical lifts over the ring of Witt vectors. In dimension 2, we establish simultaneous resolutions of singularities of these canonical lifts via $G$-Hilbert schemes. In the appendix, we discuss several approaches towards the notion of conjugacy classes for finite group schemes: This is an ingredient in McKay correspondences, but also of independent interest.
