Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of rational points on smooth projective varieties   Fix a number field k. We prove that if there is an algorithm for deciding
whether a smooth projective geometrically integral k-variety has a k-point,
then there is an algorithm for deciding whether an arbitrary k-variety has a
k-point and also an algorithm for computing X(k) for any k-variety X for which
X(k) is finite. The proof involves the construction of a one-parameter
algebraic family of Chatelet surfaces such that exactly one of the surfaces
fails to have a k-point.

5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat