Cotilting duality for Artinian rings
Francesca Mantese, Lorenzo Martini
TL;DR
This paper extends Morita-Azumaya duality results to cotilting bimodules, analyzing the dualities they induce in the derived categories of Artinian rings.
Contribution
It generalizes classical duality theorems to the setting of cotilting bimodules and derived categories for Artinian rings.
Findings
Duality represented by cotilting bimodules analyzed in derived categories
Extension of Morita-Azumaya duality to cotilting context
Characterization of dualities via cotilting bimodules in Artinian rings
Abstract
A classical result due to Morita and Azumaya establishes that given two arbitrary rings, any duality between their finitely generated modules is representable by a faithfully balanced bimodule which is a finitely generated injective cogenerator of both rings and, equivalently, these latter are one-sided artinian. We extend this well-known result to the case of a cotilting bimodule, by analysing the duality it represents in the bounded derived categories of the given rings.
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