Wojciech Chachólski: Injective resolutions in relative homological algebra

The construction of injective resolutions for bounded chain complexes over an arbitrary commutative ring is very classical, but it is only in the late eighties that Spaltenstein gave a first construction for unbounded chain complexes. A more conceptual interpretation for basically the same construction was then given five years later by Bökstedt and Neeman by studying homotopy limits in derived categories. 

In the talk I will explain the limitations of this classical constriction for  the relative homological algebra.  If  the notion of injectivity is changed, then one can obtain an  analogous result  only in the case the ring is Noetherian of finite Krull dimension.

This is a join work with Neeman, Pitsch, and Scherer,