2025/09/16 by Mizuno, Yuki
#14A22 #16S38 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2509.13073
In this paper, we introduce the notions of dualizing complexes and balanced dualizing complexes over ℤ-algebras. We prove that a noetherian connected ℤ-algebra A admits a balanced dualizing complex if and only if A satisfies Artin-Zhang's χ-condition, has finite local cohomology dimension, and possesses symmetric derived torsion as a bigraded A-A-bimodule. As an application of our study of dualizing complexes, we show that any smooth noncommutative projective scheme associated to a ℤ-algebra with a balanced dualizing complex admits a Serre functor.