有理函数Berkovich分支轨迹的拓扑与几何，II
Topology and Geometry of the Berkovich Ramification Locus for Rational Functions, II
摘要：
本文是关于非常数有理函数f：P^1 -> P^1的布氏分支轨迹系列文章的第二部分。本文证明了f的分歧轨迹包含在临界点的连通壳周围的有限半径的强管状邻域中当且仅当f在所有临界点上都是tamely分歧的。当基域具有特征零时，该界限可以被选择为仅取决于残差特征。我们给出了两个应用经典的非阿基米德分析，包括一个新版本的罗尔定理的有理函数。
英文摘要：
This article is the second installment in a series on the Berkovich ramification locus for nonconstant rational functions f: P^1 -> P^1. Here we show the ramification locus of f is contained in a strong tubular neighborhood of finite radius around the connected hull of the critical points if and only if f is tamely ramified at all of its critical points. When the ground field has characteristic zero, this bound may be chosen to depend only on the residue characteristic. We give two applications to classical non-Archimedean analysis, including a new version of Rolle's theorem for rational functions.
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