Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A counterexample to the local-global principle of linear dependence for
  abelian varieties
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin