Serre duality for dg-algebras

TL;DR

This paper extends Serre duality to noncommutative spaces linked with dg-algebras, providing new duality results, finiteness properties, and generalizations of dualizing complexes in this setting.

Contribution

It generalizes Yekutieli-Zhang's Serre duality to dg-algebras and introduces a broader notion of balanced dualizing complexes for noncommutative spaces.

Findings

Established noncommutative Serre duality for dg-algebras

Proved finiteness properties of derived global sections

Generalized the concept of balanced dualizing complexes

Abstract

We generalize Yekutieli-Zhang's noncommutative Serre Duality Theorem to the setting of noncommutative spaces associated to dg-algebras. As an application, we establish some finiteness properties of derived global sections over such noncommutative spaces. Along the way, we generalize Yekutieli's notion of a balanced dualizing complex to the setting of dg-algebras and establish some cases in which they exist.