5 papers
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…
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…
The multigraded BGG correspondence in Macaulay2
Maya Banks, Michael K. Brown, Tara Gomes +3
We give an overview of a Macaulay2 package for computing with the multigraded BGG correspondence. This software builds on the package BGG due to Abo-Decker-Eisenbud-Schreyer-Smith-…
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…
Orlov's Theorem for dg-algebras
Michael K. Brown, Prashanth Sridhar
A landmark theorem of Orlov relates the singularity category of a graded Gorenstein algebra to the derived category of the associated noncommutative projective scheme. We generaliz…