2017/01/26 by Kamran Divaani-Aazar, Divaani-Aazar, Kamran, Hossein Faridian +3
Mathematics · #13C05 #13D07 #13D45 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1701.07727
openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a Serre class S of modules, we compare the containment of the Koszul homology, Ext modules, Tor modules, local homology, and local cohomology in S up to a given bound s ≥ 0. As some applications, we give a full characterization of noetherian local homology modules. Further, we establish a comprehensive vanishing result which readily leads to the formerly known descriptions of the numerical invariants width and depth in terms of Koszul homology, local homology, and local cohomology. Also, we immediately recover a few renowned vanishing criteria scattered about the literature.