Pseudo-dualizing complexes and pseudo-derived categories

Positselski, Leonid

Rendiconti del Seminario Matematico della Università di Padova, Tome 143 (2020), pp. 153-225.

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 [45].

Classification : 16, 18
Mots-clés : Coderived categories, contraderived categories, triangulated functors, dualizing complexes, dedualizing complexes, Auslander and Bass classes, resolving and coresolving subcategories, deconstructible classes