Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Flat modules over valuation rings
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs