Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Espaces de Berkovich sur Z : \'etude locale   We investigate the local properties of Berkovich spaces over Z. Using
Weierstrass theorems, we prove that the local rings of those spaces are
noetherian, regular in the case of affine spaces and excellent. We also show
that the structure sheaf is coherent. Our methods work over other base rings
(valued fields, discrete valuation rings, rings of integers of number fields,
etc.) and provide a unified treatment of complex and p-adic spaces.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
32
The categories of this paper are: atom-ph