2024/04/12 by Kostiantyn Iusenko, Iusenko, Kostiantyn, Eduardo N. Marcos +4
Mathematics · Medicine · #13B10 (Secundary) #13D05 #18G25(Primary) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #K-Theory and Homology (math.KT) #math.AC #math.KT #msc:13B10 #msc:13D05
paper · pdf · doi:10.48550/arxiv.2404.08534
Final version, to be published in Proceedings of the American Mathematical Society. Some corrections following the referee report
openalex publication_date 2024/04/12 · openalex created_date 2025/10/10 · arxiv created 2026/07/29 · arxiv updated 2026/07/30 · openalex updated_date 2026/08/01
We investigate the relationship between smoothness and the relative global dimension of a ring extension. We prove that a smooth commutative algebra A over B has finite relative global dimension gdim(A,B). Conversely, under a mild condition on B, the finiteness of gdim(A,B) implies that the map B → A is smooth. We also relate the relative global dimension to the usual global dimension of the fibers of B → A, and establish a formula for the relative global dimension of tensor products of extensions. Finally, we present examples and an alternative characterisation of smoothness in terms of relative Hochschild homology.