贝尔科维奇的作品非常出色
Les espaces de Berkovich sont excellents
摘要：
本文首先从交换代数的角度研究了Berkovich解析空间的局部环。我们证明这些环是优秀的;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，也包括完全非阿基米德域的任何完全扩张的情形），并证明了通常的交换代数性质（Rm，Sm，Gorenstein，Cohen-Macaulay，Complete Intersection）在解析可分基域扩张下是稳定的;对于仿射代数上的任意一个生成格式，我们还建立了一个GAGA原理。第二部分的文件涉及更多的全球几何概念：我们定义，显示存在和建立基本性质的不可约组成部分的解析空间;我们定义，显示存在和建立基本性质的规范化;我们研究的行为连通性和不可约的基础变化。
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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