Generalized tilting theory
Pedro Nicolas, Manuel Saorin
TL;DR
This paper investigates conditions under which dg bimodules induce triangle equivalences between derived categories, connecting recent advances in tilting theory, homological epimorphisms, and recollements.
Contribution
It provides necessary and sufficient criteria for dg bimodules to produce derived category equivalences, extending recent research in tilting and homological algebra.
Findings
Established criteria for triangle equivalences via dg bimodules
Connected tilting modules with homological epimorphisms and recollements
Extended existing theories in derived categories and tilting modules
Abstract
We study necessary and sufficient conditions for a dg bimodule to yield triangle equivalences between (quotients of) the corresponding derived categories. This is related to recent work by Bazzoni-Mantese-Tonolo, Yang, Angeleri H\"ugel-Koenig-Liu, Chen-Xi, Bazzoni-Pavarin,... on large tilting modules, homological epimorphisms and recollements.
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