Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite descent obstruction and non-abelian reciprocity   For a nice algebraic variety $X$ over a number field $F$, one of the central
problems of Diophantine Geometry is to locate precisely the set $X(F)$ inside
$X(\A_F)$, where $\A_F$ denotes the ring of ad\`eles of $F$. One approach to
this problem is provided by the finite descent obstruction, which is defined to
be the set of adelic points which can be lifted to twists of torsors for
(certain) finite \'etale group schemes over $F$ on $X$. More recently, Kim
proposed an iterative construction of another subset of $X(\A_F)$ which
contains the set of rational points. In this paper, we compare the two
constructions. Our main result shows that the two approaches are essentially
equivalent.

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The categories of this paper are: stat
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex