HOMOLOGICALLY TRIVIAL ACTIONS ON CHAIN COMPLEXES AND FINITENESS PROPERTIES OF INFINITE GROUPS

Let R be a commutative, Noetherian ring and let GAMMA be a discrete group. A generalization of Swan's classical technique of grafting chain complexes shows that GAMMA is of type FP(infinity) over R if and only if there is a chain complex C* of finitely generated projective RGAMMA-modules, augmented by R, such that each H(i)(C) is finitely generated over R and trivial over GAMMA.