Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: $F$-purity deforms in $\mathbb{Q}$-Gorenstein rings
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph