Quasi-Gorenstein morphisms of commutative local dg-algebras

TL;DR

This paper introduces quasi-Gorenstein morphisms for commutative local dg-algebras and characterizes them using a Gorenstein virtually small property, extending known results to local rings.

Contribution

It presents a new characterization of quasi-Gorenstein morphisms and relates them to exact sequences in noetherian local rings, expanding the theoretical framework.

Findings

Characterization of quasi-Gorenstein morphisms using Gorenstein virtually small property.

Extension of results to homomorphisms of local rings.

Characterization of exact sequences via quasi-Gorenstein morphisms involving Koszul complexes.

Abstract

We introduce quasi-Gorenstein morphisms of commutative local dg-algebras and use a Gorenstein version of the virtually small property to characterize them, a result which is new even for homomorphisms of local rings. In a different direction, we characterize exact sequences in a noetherian local ring, in the sense of Avramov, Henriques, and \c{S}ega, in terms of quasi-Gorenstein morphisms involving Koszul complexes.