Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Reductions of non-lc ideals and non $F$-pure ideals assuming weak
  ordinarity
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th