Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular Embeddings and Rigidity for Fuchsian Groups   We prove a rigidity theorem for semi-arithmetic Fuchsian groups: If
$\Gamma_1$, $\Gamma_2$ are two semi-arithmetic lattices in
$\mathrm{PSL}(2,\mathbb{R})$ virtually admitting modular embeddings and
$f\colon\Gamma_1\to\Gamma_2$ is a group isomorphism that respects the notion of
congruence subgroups, then $f$ is induced by an inner automorphism of
$\mathrm{PGL}(2,\mathbb{R})$.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org