RELATIVE INJECTIVE RESOLUTIONS VIA TRUNCATIONS, PART II

In the rst part of this paper we reinterpreted the by now classical result of Spal- tenstein or Bokstedt and Neeman of the construction of injective resolutions for unbounded chain complexes: There is a model category of towers of bounded chain complexes which forms a model approximation for unbounded chain complexes. We now wonder in this part whether this point of view can be relativized, i.e. if the same category of towers forms a model approximation for un- bounded complexes, but where one changes the weak equivalences (formerly quasi-isomorphisms) to W-equivalences, where W is a class of injective modules. We prove that this approach is valid for any injective class if and only if we work over a Noetherian ring of nite Krull dimension.