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].
DOI : 10.4171/RSMUP/44
Mots-clés : Coderived categories, contraderived categories, triangulated functors, dualizing complexes, dedualizing complexes, Auslander and Bass classes, resolving and coresolving subcategories, deconstructible classes
@article{RSMUP_2020__143__153_0,
author = {Positselski, Leonid},
title = {Pseudo-dualizing complexes and pseudo-derived categories},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {153--225},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {143},
year = {2020},
doi = {10.4171/RSMUP/44},
mrnumber = {4103744},
zbl = {1505.16008},
url = {http://www.numdam.org/articles/10.4171/RSMUP/44/}
}
TY - JOUR AU - Positselski, Leonid TI - Pseudo-dualizing complexes and pseudo-derived categories JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2020 SP - 153 EP - 225 VL - 143 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/44/ DO - 10.4171/RSMUP/44 ID - RSMUP_2020__143__153_0 ER -
%0 Journal Article %A Positselski, Leonid %T Pseudo-dualizing complexes and pseudo-derived categories %J Rendiconti del Seminario Matematico della Università di Padova %D 2020 %P 153-225 %V 143 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/44/ %R 10.4171/RSMUP/44 %F RSMUP_2020__143__153_0
Positselski, Leonid. Pseudo-dualizing complexes and pseudo-derived categories. Rendiconti del Seminario Matematico della Università di Padova, Tome 143 (2020), pp. 153-225. doi : 10.4171/RSMUP/44. http://www.numdam.org/articles/10.4171/RSMUP/44/
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