Harmonic cocycles and cohomology of arithmetic groups (in positive characteristic)
| dc.creator | Reversat, Marc | |
| dc.date | 1999-10-07 | |
| dc.date.accessioned | 2026-07-07T05:31:23Z | |
| dc.date.available | 2026-07-07T05:31:23Z | |
| dc.description | Let $K$ be a global field of characteristic $p>0$. We study the cohomology of arithmetic subgroups $Γ$ 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 $Γ$ with compact supports and values in ${\Bbb Z}[1/p]$, and we relate it to spaces of harmonic cocycles, also with compact supports (§3). We give a description of the locus of these supports, in particular by introducing a notion of cusp in dimension $n\geq 1$ (§4) and we calculate "geometrically" the Euler-Poincaré characteristic of this cohomology, up to torsion (§5). | |
| dc.identifier | https://arxiv.org/abs/math/9910190 | |
| dc.identifier | http://arxiv.org/abs/math/9910190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79321 | |
| dc.subject | Number Theory | |
| dc.title | Harmonic cocycles and cohomology of arithmetic groups (in positive characteristic) | |
| dc.type | text |