HOMOLOGICAL DIMENSIONS OF UNBOUNDED COMPLEXES

This paper explores various notions of projective, injective, and flat dimensions, arising from recent constructions of resolutions of unbounded complexes, proposed by N. Spaltenstein and by S. Halperin with the authors. The different versions of each dimension are compared to each other, and also to the classical concepts, whenever these may be defined. Cohomological characterizations of the dimensions are provided in terms of vanishing of appropriate derived functors. The behavior of the dimensions under change of rings is investigated.