2025/06/03 by Brown, Michael K., Levins, Andrew J. Soto, Sridhar, Prashanth · 1 citation
#14F08 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2506.02398
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.