Existence of balanced dualizing dg-modules

TL;DR

This paper establishes cohomological criteria for the existence of balanced dualizing dg-modules, extending Van den Bergh's theorem, and links dg-algebra properties to their zeroth cohomology in the context of Serre duality.

Contribution

It generalizes Van den Bergh's theorem to dg-algebras and provides new examples of dg-algebras satisfying Serre duality.

Findings

Cohomological conditions for balanced dualizing dg-modules

Equivalence between existence of dualizing dg-modules and dualizing complexes on zeroth cohomology

New examples of dg-algebras with Serre duality

Abstract

We describe cohomological conditions that are necessary and sufficient for the existence of balanced dualizing dg-modules, generalizing a theorem of Van den Bergh for balanced dualizing complexes over graded algebras. As a consequence, we show that a dg-algebra satisfying certain finiteness conditions admits a balanced dualizing dg-module if and only if its zeroth cohomology algebra admits a balanced dualizing complex. Additionally, we obtain a host of new examples of dg-algebras whose associated noncommutative spaces satisfy Serre duality.