Pseudo-dualizing complexes and pseudo-derived categories
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 arXiv:1503.05523.
Cite
@article{arxiv.1703.04266,
title = {Pseudo-dualizing complexes and pseudo-derived categories},
author = {Leonid Positselski},
journal= {arXiv preprint arXiv:1703.04266},
year = {2025}
}
Comments
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.7: misprints corrected, references updated -- this is intended as the final version; v.8: TeXnical mistake with shifted numbering of theorems in the Appendix corrected