Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability in the high-dimensional cohomology of congruence subgroups   We prove a representation stability result for the codimension-one cohomology
of the level three congruence subgroup of $\mathbf{SL}_n(\mathbb{Z})$. This is
a special case of a question of Church-Farb-Putman which we make more precise.
Our methods involve proving several finiteness properties of the Steinberg
module for the group $\mathbf{SL}_n(K)$ for $K$ a field. This also lets us give
a new proof of Ash-Putman-Sam's homological vanishing theorem for the Steinberg
module. We also prove an integral refinement of Church-Putman's homological
vanishing theorem for the Steinberg module for the group
$\mathbf{SL}_n(\mathbb{Z})$.

14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph