Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Th\'eorie inverse de Galois sur les corps des fractions rationnelles
  tordus   In this article, we prove that if $H$ is a skew field of center $k$ and
$\sigma$ an automorphism of finite order of $H$ such that the fixed subfield
$k^{\langle \sigma \rangle}$ of $k$ under the action of $\sigma$ contains an
ample field, then the inverse Galois problem has a positive answer over the
skew field $H(t,\sigma)$ of twisted rational fractions. Moreover, if
$k^{\langle \sigma \rangle}$ contains either a real closed field, or an
Henselian field of residue characteristic $0$ and containing all roots of
unity, then the profree group of countable rank $\widehat{F}_{\omega}$ is a
Galois group over $H(t,\sigma)$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
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The categories of this paper are: supr-con
3
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: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc