Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic cocycles and cohomology of arithmetic groups (in positive
  characteristic)   Let $K$ be a global field of characteristic $p>0$. We study the cohomology of
arithmetic subgroups $\Gamma $ of $SL_{n+1}(K)$ (with respect to a fixed place
of $K$), under the hypothesis that these groups have no $p'$-torsion (any
arithmetic group possesses a normal subgroup of finite index without
$p'$-torsion). We define the cohomology of $\Gamma $ with compact supports and
values in ${\Bbb Z}[1/p]$, and we relate it to spaces of harmonic cocycles,
also with compact supports (\S 3). We give a description of the locus of these
supports, in particular by introducing a notion of cusp in dimension $n\geq 1$
(\S 4) and we calculate "geometrically" the Euler-Poincar\'e characteristic of
this cohomology, up to torsion (\S 5).

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an