Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Tight closure with respect to a multiplicatively closed subset of an
  $F$-pure local ring
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess