Non-archimedean orbifolds covered by mumford curves
Non-archimedean orbifolds covered by mumford curves
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DOI：
10.1090/s1056-3911-04-00384-4
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发表时间：
2005
影响因子：
1.8
通讯作者：
Fumiharu Kato
中科院分区：
文献类型：
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作者：
Fumiharu Kato
在这篇文章中，我们发展了一种所谓的芒福德奥比诺兹理论，即。被Mumford曲线覆盖的刚体解析的奥比诺德。给出了治疗这类耳垂的一般方法。主要结果给出了群的分解图实现为离散群的一个充要条件，这对于构造几个有趣的非阿基米德离散群是有用的，如p-进三角群1.导言。就像在经典的黎曼曲面理论中一样，在刚性解析几何中研究代数/解析曲线也应该是有用的。刚性解析奥布洛德理论应该为研究曲线的几何提供一种实用的方法，特别是通过将它们反映在(分支的)Galois覆盖中来分析它们的对称性(自同构)，这例如导致理解曲线的模层化。此外，这样的理论在线性微分方程组理论中也应该是成功的，特别是在可视化它们的单调现象方面，就像在经典背景下的情况一样(参见[23]，以获得极好的解释)。在这篇文章中，我们的目的是讨论所谓的Mumford orborold的基本几何，它可能是刚性解析几何中最重要的orborold类之一，以及相关离散群的构造。让我们更精确地解释它：设K是具有非平凡赋值的代数闭完全非阿基米德赋值域。我们的概念取材于Yves André提出的p-ADDIC ORBORBOLD(参看[1，§5])：
In this article we develop a theory of the socalled Mumford orbifolds, viz. rigid-analytic orbifolds covered by Mumford curves. General recipe for treating such orbifolds is given. The main result states a necessary and sufficient condition for abstruct graphs of groups to be realized as discrete groups for Mumford orbifolds, which is useful for constructing several interesting non-archimedean discrete groups, such as p-adic triangle groups.1. Introduction. Like in the classical theory of Riemann surfaces the orbifold technique should be useful also in rigid analytic geometry for studying algebraic/analytic curves. The theory of rigid analytic orbifolds should provide a practical method for studying geometry of curves, especially for analyzing their symmetries (automorphisms) by reflecting them in (ramified) Galois coveringes, which leads for instance to understanding of the stratification of moduli of curves. Moreover, such a theory should be successful also in the theory of linear differential equations, especially in visualizing their monodromy phenomena, as it was the case in the classical setting (cf.[23] for an excellent account). Our objective in this article is to discuss the basic geometry of the so-called Mumford orbifolds, which are perhaps among the most practically important classes of orbifolds in rigid analytic geometry, and the construction of the related discrete groups. Let us be more precise in explaining it: Let K be an algebraically closed complete non-archimedean valued field with a non-trivial valuation. Our notion of orbifold is taken up from the p-adic orbifolds introduced by Yves André (cf.[1, § 5]):