Le complexe de chaînes dʹun G-complexe simplicial acyclique

Résumé Let G be a finite group. The main result of this note shows that the reduced chain complex of an acyclic finite dimensional simplicial G-complex is a split acyclic complex of G-modules. The proof requires the extension of well known results on finitely generated p-permutation modules to arbitrary p-permutation modules. The key is a theorem stating that a bounded complex of p-permutation modules is split acyclic if and only if all its Brauer quotients are acyclic.