Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonabelian Cohen-Lenstra Moments   In this paper we give a conjecture for the average number of unramified
$G$-extensions of a quadratic field for any finite group $G$. The Cohen-Lenstra
heuristics are the specialization of our conjecture to the case that $G$ is
abelian of odd order. We prove a theorem towards the function field analog of
our conjecture, and give additional motivations for the conjecture including
the construction of a lifting invariant for the unramified $G$-extensions that
takes the same number of values as the predicted average and an argument using
the Malle-Bhargava principle. We note that for even $|G|$, corrections for the
roots of unity in $\mathbb{Q}$ are required, which can not be seen when $G$ is
abelian.

10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ