2002/12/09 by H. -B. Foxby, Hans-Bj�rn Foxby, Srikanth B. Iyengar +3 · 2 citations
Mathematics · #13C15 #13C25 (Primary) #13D45 (Secondary) #18G15 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AG #msc:13C15 #msc:13C25 #msc:13D45 #msc:18G15
paper · pdf · doi:10.48550/arxiv.math/0212125
19 pages. To be published in: Commutative Algebra. Its interaction with Algebraic Geometry (Grenoble-Lyon 2001), Contemporary Math
arxiv created 2002/12/09 · openalex publication_date 2002/12/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that over a commutative noetherian ring the three approaches to introducing depth for complexes: via Koszul homology, via Ext modules, and via local cohomology, all yield the same invariant. Using this result, we establish a far reaching generalization of the classical Auslander-Buchsbaum formula for the depth of finitely generated modules of finite projective dimension. We extend also Iversen's amplitude inequality to unbounded complexes. As a corollary we deduce: Given a local homomorphism Q-->R, if there is a non-zero finitely generated R-module that has finite flat dimension both over Q and over R, then the flat dimension of R over Q is finite. This last result yields a module theoretic extension of a characterization of regular local rings in characteristic p due to Kunz and Rodicio