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摘要翻译：
本文首先从交换代数的角度研究了Berkovich解析空间的局部环。我们表明那些环是优秀的；我们引入了非阿基米德完全域的解析可分扩张的概念（它包括有限可分扩张的情形，也包括完全完全非阿基米德完全域的任意完全扩张的情形），并证明了通常的交换代数性质(Rm，Sm，Gorenstein，Cohen-Macaulay，完全交）在解析可分的基域扩张下是稳定的；对于仿拟代数上的有限生成格式，我们也建立了关于这些性质的GAGA原理。第二部分讨论了更多的全局几何概念：定义、证明了解析空间不可约成分的存在性并建立了其基本性质；我们定义了它的归一化，证明了它的存在性，并建立了它的基本性质；我们还研究了连通性和不可约性对碱基变化的影响。
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英文标题：
《Les espaces de Berkovich sont excellents》
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作者：
Antoine Ducros
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最新提交年份：
2009
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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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英文摘要：
In this paper, we first study the local rings of a Berkovich analytic space from the point of view of commutative algebra. We show that those rings are excellent ; we introduce the notion of a an analytically separable extension of non-archimedean complete fields (it includes the case of the finite separable extensions, and also the case of any complete extension of a perfect complete non-archimedean field) and show that the usual commutative algebra properties (Rm, Sm, Gorenstein, Cohen-Macaulay, Complete Intersection) are stable under analytically separable ground field extensions; we also establish a GAGA principle with respect to those properties for any finitely generated scheme over an affinoid algebra. A second part of the paper deals with more global geometric notions : we define, show the existence and establish basic properties of the irreducible components of analytic space ; we define, show the existence and establish basic properties of its normalization ; and we study the behaviour of connectedness and irreducibility with respect to base change.
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PDF链接：
https://arxiv.org/pdf/0706.0666
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