Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integral Hasse principle and strong approximation for Markoff surfaces   We study the failure of the integral Hasse principle and strong approximation
for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer-Manin
obstruction.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org