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摘要翻译：
我们在这里研究数域的整数环上的Berkovich线。它是一个自然的对象，包含与每个地方相关联的复杂的非阿基米德分析空间。我们证明了这条直线满足良好的拓扑和代数性质，并给出了它所包含的Stein空间的几个例子。我们在收敛算术幂级数的研究中得到了应用：零点和极点的选择，整体环的无以太性和Galois逆问题。用开复单位圆盘上的解析函数给出了这类幂级数的典型例子，其泰勒展开在0中具有整数系数。
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英文标题：
《La droite de Berkovich sur Z》
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作者：
J\'er\^ome Poineau
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
We study here the Berkovich line over the ring of integers of a number field. It is a natural object which contains complex and non-Archimedean analytic spaces associated to each place. We prove that this line satisfies good topological and algebraic properties and exhibit a few examples of Stein spaces that lie in it. We derive applications to the study of convergent arithmetic power series: choice of zeroes and poles, noetherianity of global rings and inverse Galois problem. Typical examples of such power series are given by analytic functions on the open complex unit disk whose Taylor development in 0 has integer coefficients.
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PDF链接：
https://arxiv.org/pdf/0809.2880
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