Wild Ramification in the Imperfect Residue Field Case
Wild Ramification in the Imperfect Residue Field Case
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不完美残基场案例中的疯狂后果
DOI：
10.2969/aspm/01210287
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
Osamu Hyodo
中科院分区：
文献类型：
--
作者：
Osamu Hyodo
本文的目的是研究完全离散赋值域的野分支，而不是假设剩余域是完美的。在剩余域是完美的情况下，有一个美丽的分支群理论(Serre[14]§4)。我们案件的困难之处在于，似乎总体上没有这样的理论。作为我们研究的应用，我们将展示以下三个结果。设K是具有混合特征(0，p)的完全离散赋值域。(1)Miki[9]，[10]研究了K的ZP-扩张，他证明了K的任何ZP-扩张都包含在K的未分枝扩张和K的“正则子域”k的ZP-扩张的复合体中。
The aim of this paper is to study wild ramification of complete discrete valuation fields without the assumption that the residue field is perfect. In the case where the residue field is perfect, there is a beautiful theory of ramification groups (Serre [14] §4). The difficulty of our case is that there seems to be no such a theory in general. As applications of our study, we shall show the following three results. In the following, let K be a complete discrete valuation field of mixed characteristics (0, p). (1) Miki [9], [10] studied ZP-extensions of K. He showed that any ZP-extension of K is contained in a composite of an unramified extension of K and a ZP-extension of the "canonical subfield" k of K. Here, k is characterized by the following properties.