The Stable Derived Category of a Ring via Model Categories.

摘要

Let R be a ring. The stable derived category S(R) is defined as the full subcategory of exact complexes of the homotopy category of chain complexes of injective R-modules, in the case that R is a Noetherian ring. We define a model structure over Ch (R), the category of chain complexes of R-modules, such that its homotopy category is precisely S(R). This construction allows us to remove the Noetherian condition on the ring and gives us a better and more transparent understanding of the properties of S( R).