Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zariski compactness of minimal spectrum and flat compactness of maximal
  spectrum   In this article, Zariski compactness of the minimal spectrum and flat
compactness of the maximal spectrum are characterized.

10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org