Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois groups and cohomological functors   Let $q=p^s$ be a prime power, $F$ a field containing a root of unity of order
$q$, and $G_F$ its absolute Galois group. We determine a new canonical quotient
$\mathrm{Gal}(F_{(3)}/F)$ of $G_F$ which encodes the full mod-$q$ cohomology
ring $H^*(G_F,\mathbb{Z}/q)$ and is minimal with respect to this property. We
prove some fundamental structure theorems related to these quotients. In
particular, it is shown that when $q=p$ is an odd prime, $F_{(3)}$ is the
compositum of all Galois extensions $E$ of $F$ such that $\mathrm{Gal}(E/F)$ is
isomorphic to $\{1\}$, $\mathbb{Z}/p$ or to the nonabelian group $H_{p^3}$ of
order $p^3$ and exponent $p$.

14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph