Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The point counting problem in representation varieties of torus knots   We compute the motive of the variety of representations of the torus knot of
type (m,n) into the affine groups $AGL_1$ and $AGL_2$ for an arbitrary field
$k$. In the case that $k = F_q$ is a finite field this gives rise to the count
of the number of points of the representation variety, while for $k = C$ this
calculation returns the E-polynomial of the representation variety. We discuss
the interplay between these two results in sight of Katz theorem that relates
the point count polynomial with the E-polynomial. In particular, we shall show
that several point count polynomials exist for these representation varieties,
depending on the arithmetic between m,n and the characteristic of the field,
whereas only one of them agrees with the actual E-polynomial.

8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg