JournalsrsmupVol. 143pp. 153–225

Pseudo-dualizing complexes and pseudo-derived categories

  • Leonid Positselski

    Czech Academy of Sciences, Prague, Czech Republic, National Research University, Moscow, Russia and University of Haifa,
Pseudo-dualizing complexes and pseudo-derived categories cover
Download PDF

A subscription is required to access this article.

Abstract

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].

Cite this article

Leonid Positselski, Pseudo-dualizing complexes and pseudo-derived categories. Rend. Sem. Mat. Univ. Padova 143 (2020), pp. 153–225

DOI 10.4171/RSMUP/44