Depth and amplitude for unbounded complexes

dc.creatorFoxby, H. -B.
dc.creatorIyengar, S.
dc.date2002-12-09
dc.date.accessioned2026-07-07T04:53:38Z
dc.date.available2026-07-07T04:53:38Z
dc.descriptionWe 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
dc.description19 pages. To be published in: Commutative Algebra. Its interaction with Algebraic Geometry (Grenoble-Lyon 2001), Contemporary Math
dc.identifierhttps://arxiv.org/abs/math/0212125
dc.identifierhttp://arxiv.org/abs/math/0212125
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65932
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13C15; 13C25 (Primary), 18G15; 13D45 (Secondary)
dc.titleDepth and amplitude for unbounded complexes
dc.typetext

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