Pseudo-dualizing complexes and pseudo-derived categories

The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions. In the specific setting of a pair of associative rings, we show that the datum of a pseudo-dualizing complex induces a triangulated equivalence between a pseudo-coderived category and a pseudo-contraderived category. The latter terms mean triangulated categories standing "in between" the conventional derived category and the coderived or the contraderived category. The constructions of these triangulated categories use appropriate versions of the Auslander and Bass classes of modules. The constructions of derived functors providing the triangulated equivalence are based on a generalization of a technique developed in our previous paper arXiv:1503.05523.Comment: LaTeX 2e with pb-diagram, xy-pic, and tikz-cd, 60 pages, 14+3 commutative diagrams; v.4: sections 10-12 added, new subsections 0.8 and 0.10 inserted in the Introduction; v.5: subsection 0.2 shortened, basic definitions added in section 1, explanations added in the proof of Theorem 4.2, several references added; v.7: misprints corrected, references updated -- this is intended as the final versio