Explicit resolution of weak wild quotient singularities on arithmetic surfaces
Explicit resolution of weak wild quotient singularities on arithmetic surfaces
复制标题
算术曲面上弱野商奇点的显式解析
DOI：
10.1090/jag/745
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Wewers
中科院分区：
文献类型：
--
作者：
Andrew Obus;S. Wewers
一个弱的野生算术商奇异性产生于一个光滑算术曲面的有限群作用的商，其中闭特征p纤维上一点的惯性群是一个具有最小可能分支跳的p-群。在本文中，我们给出了完整的显式决议，这些奇异性的变形理论和估值理论，采取更本地的角度比以前的工作已经采取。我们的描述回答了Lorenzini的几个问题。沿着这一思路，我们给出了离散域上P^1的正规snc-模型正则的赋值理论判据。
A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed characteristic p fiber is a p-group acting with smallest possible ramification jump. In this paper, we give complete explicit resolutions of these singularities using deformation theory and valuation theory, taking a more local perspective than previous work has taken. Our descriptions answer several questions of Lorenzini. Along the way, we give a valuation-theoretic criterion for a normal snc-model of P^1 over a discretely valued field to be regular.