Rigidity, reduction, and ramification
Rigidity, reduction, and ramification
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刚性、减少和衍生
DOI：
10.1007/s00208-003-0441-x
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发表时间：
2003
影响因子：
1.4
通讯作者：
R. Pries
中科院分区：
文献类型：
--
作者：
I. Bouw;R. Pries
本文考虑曲线的广分支g -伽罗盖：Y→1在特征代数闭域上恰好有一点分支。与aporpsl2 (p)相同，我们证明了Abhyankar的惯性猜想，即对于这样的覆盖，所有可能的惯性群都在无穷远上出现。此外，我们还证明了可实现的导体集合依赖于群。我们使用的方法是计算在3点分支的伽罗瓦覆盖的约简。我们观察到在特征点上具有给定惯性的覆盖的存在性与特征点上覆盖的算法密切相关。
In this paper we consider wildly ramifiedG-Galois covers of curvesf:Y→ℙ1kbranched at exactly one point over an algebraically closed fieldkof characteristicp. ForGequal toAporPSL2(p), we prove Abhyankar's Inertia Conjecture that all possible inertia groups occur over infinity for such coversf. In addition, we prove that the set of conductors that can be realized depends on the group. The method we use is to compute the reduction of Galois covers ofbranched at 3 points. We observe that the existence of covers with given inertia in characteristicpis closely related to the arithmetic of covers in characteristic zero.