Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparing descent obstruction and Brauer-Manin obstruction for open
  varieties   We provide a relation between Brauer-Manin obstruction and descent
obstruction for torsors over open varieties under a connected linear algebraic
group or a group of multiplicative type is given. Such a relation is further
refined for torsors under a torus. As an appliaction, we prove that the
semi-simple part of a connected linear algebraic group will satisfy strong
approximation with Brauer-Manin obstruction if G iteself satisfies strong
approximation with Brauer-Manin obstruction.The equivalence between descent
obstruction and etale Brauer-Manin obstruction for smooth projective varieties
is extended to smooth quasi-projective varieties, which provides the
perspective to study integral points.

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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th