Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Les espaces de Berkovich sont excellents   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.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph