Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Fields of rationality for automorphic representations   This paper proves two results on the field of rationality $\Q(\pi)$ for an
automorphic representation $\pi$, which is the subfield of $\C$ fixed under the
subgroup of $\Aut(\C)$ stabilizing the isomorphism class of the finite part of
$\pi$. For general linear groups and classical groups, our first main result is
the finiteness of the set of discrete automorphic representations $\pi$ such
that $\pi$ is unramified away from a fixed finite set of places, $\pi_\infty$
has a fixed infinitesimal character, and $[\Q(\pi):\Q]$ is bounded. The second
main result is that for classical groups, $[\Q(\pi):\Q]$ grows to infinity in a
family of automorphic representations in level aspect whose infinite components
are discrete series in a fixed $L$-packet under mild conditions.

15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int