Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting points of schemes over finite rings and counting
  representations of arithmetic lattices   We relate the singularities of a scheme $X$ to the asymptotics of the number
of points of $X$ over finite rings. This gives a partial answer to a question
of Mustata. We use this result to count representations of arithmetic lattices.
More precisely, if $\Gamma$ is an arithmetic lattice whose $\mathbb{Q}$-rank is
greater than one, let $r_n(\Gamma)$ be the number of irreducible
$n$-dimensional representations of $\Gamma$ up to isomorphism. We prove that
there is a constant $C$ (for example, $C=746$ suffices) such that
$r_n(\Gamma)=O(n^C)$ for every such $\Gamma$. This answers a question of Larsen
and Lubotzky.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics