Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Very strong approximation for certain algebraic varieties   Let F be a global field. In this work, we show that the Brauer-Manin
condition on adelic points for subvarieties of a torus T over F cuts out
exactly the rational points, if either F is a function field or, if F is the
field of rational numbers and T is split. As an application, we prove a
conjecture of Harari-Voloch over global function fields which states, roughly
speaking, that on any rational hyperbolic curve, the local integral points with
the Brauer-Manin condition are the global integral points. Finally we prove for
tori over number fields a theorem of Stoll on adelic points of zero-dimensional
subvarieties in abelian varieties.

11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas