Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting points on $\text{Hilb}^m\mathbb{P}^2$ over function fields   Let $K$ be a global field of positive characteristic. We give an asymptotic
formula for the number of $K$-points of bounded height on the Hilbert scheme
$\text{Hilb}^2\mathbb{P}^2$ and show that by eliminating an exceptional thin
set, the constant in front of the main term agrees with the prediction of Peyre
in the function field setting. Moreover, we extend the analogy between the
integers and $0$-cycles on a variety $V$ over a finite field to $0$-cycles on a
variety $V$ over $K$ and establish a version of the prime number theorem in the
case when $V = \mathbb{P}^2$.

7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga