### Harmonic cocycles and cohomology of arithmetic groups (in positive characteristic), by Marc Reversat

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).

Marc Reversat <reversat@picard.ups-tlse.fr>