This work reports on expanded Serre duality in dg-algebras, highlighting new finiteness properties of derived global sections.
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.
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Brown et al. (2025) studied this question.
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