Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting $3$-dimensional algebraic tori over $\mathbb{Q}$   In this paper we count the number $N_3^{\text{tor}}(X)$ of $3$-dimensional
algebraic tori over $\mathbb{Q}$ whose Artin conductor is bounded by $X$. We
prove that $N_3^{\text{tor}}(X) \ll_{\varepsilon} X^{1 + \frac{\log 2 +
\varepsilon}{\log \log X}}$, and this upper bound can be improved to
$N_3^{\text{tor}}(X) \ll X (\log X)^4 \log \log X$ under the Cohen-Lenstra
heuristics for $p=3$. We also prove that for $67$ out of $72$ conjugacy classes
of finite nontrivial subgroups of $\operatorname{GL}_3(\mathbb{Z})$, Malle's
conjecture for tori over $\mathbb{Q}$ holds up to a bounded power of $\log X$
under the Cohen-Lenstra heuristics for $p=3$ and Malle's conjecture for quartic
$A_4$-fields.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
1
The categories of this paper are: cs