Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brauer-Manin obstruction for Markoff-type cubic surfaces   Following the works by Ghosh and Sarnak; Loughran and Mitankin;
Colliot-Th\'el\`ene, Wei, and Xu, we study the local-global principle and
Brauer--Manin obstruction for integral points on similar Markoff-type cubic
surfaces. Furthermore, we construct a family of counterexamples to the integral
Hasse principle which can be explained by the Brauer--Manin obstruction with a
greater frequency, compared to the results given by Loughran and Mitankin;
Colliot-Th\'el\`ene, Wei, and Xu.

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The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph