Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Diophantine decidability for curves and Grothendieck's section
  conjecture
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics