Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Failure of strong approximation on an affine cone   We use the Brauer-Manin obstruction to strong approximation on a punctured
affine cone to explain a curious property of coprime integer solutions to a
homogeneous Diophantine equation.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg