3 papers
math.AC2026
Derived complete intersections and polynomial growth of Betti numbers over dg-algebras
Michael K. Brown, Justin Lyle
A theorem of Gulliksen states that a local ring is a complete intersection if and only if the Betti numbers of its finitely generated modules grow polynomially. We prove a derived…
math.RA2025
Existence of balanced dualizing dg-modules
Michael K. Brown, Andrew J. Soto Levins, Prashanth Sridhar
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 dual…
math.RA2024
Serre duality for dg-algebras
Michael K. Brown, Prashanth Sridhar
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 finiten…