Acyclicity of Schneider and Stuhler's coefficient systems:another approach in the level 0 case
| dc.creator | Broussous, Paul | |
| dc.date | 2003-12-09 | |
| dc.date | 2004-01-06 | |
| dc.date.accessioned | 2026-07-07T05:03:41Z | |
| dc.date.available | 2026-07-07T05:03:41Z | |
| dc.description | Let F be a non archimedean local field and G be the locally profinite group GL(N,F), N>0. We denote by X the Bruhat-Tits building of G. For all smooth complex representation V of G and for all level n>0, Schneider and Stuhler have constructed a coefficient system C = C(V, n) on the simplicial complex X. They proved that if V is generated by its fixed vectors under the principal congruence subgroup of level n, then the augmented complex of oriented chains of X with coefficients in C is a resolution of V in the category of smooth complex representations of G. In this paper we give another proof of this result, in the level 0 case, and assuming moreover that V is generated by its fixed vectors under an Iwahori subgroup I of G. Here "level 0" refers to Bushnell and Kutzko's terminology, that is to the case n=1+0. Our approach is different. We strongly use the fact that the trivial character of I is a type in the sense of Bushnell and Kutzko. | |
| dc.description | 15 pages, revised version | |
| dc.identifier | https://arxiv.org/abs/math/0312183 | |
| dc.identifier | http://arxiv.org/abs/math/0312183 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69524 | |
| dc.subject | Representation Theory | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 22E50; 18G10 | |
| dc.title | Acyclicity of Schneider and Stuhler's coefficient systems:another approach in the level 0 case | |
| dc.type | text |