Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Diophantine Approximation of non-algebraic points on varieties II:
  Explicit estimates for arithmetic Hilbert Functions
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th