Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed
  dimension
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org