Module-Theoretic Characterizations of Gorenstein Morphisms

TL;DR

This paper extends module-theoretic characterizations of Gorenstein properties from local algebra to Gorenstein morphisms and graded-commutative dg-algebras, broadening their applicability in algebraic contexts.

Contribution

It generalizes existing Gorenstein characterizations to the setting of Gorenstein morphisms and dg-algebras, providing a unified framework.

Findings

Characterizations hold for graded-commutative Gorenstein dg-algebras

Generalization to Gorenstein morphisms in the relative setting

Framework unifies local and relative Gorenstein properties

Abstract

The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined by [AF92]. We achieve this by proving these characterizations more generally for graded-commutative Gorenstein dg-algebras.