Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relating decision and search algorithms for rational points on curves of
  higher genus   For affine plane curves defined over the rationals of genus at least two, we
show that a decision algorithm for the existence of solutions also yields a
search algorithm for all solutions.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin