Depth and amplitude for unbounded complexes
| dc.creator | Foxby, H. -B. | |
| dc.creator | Iyengar, S. | |
| dc.date | 2002-12-09 | |
| dc.date.accessioned | 2026-07-07T04:53:38Z | |
| dc.date.available | 2026-07-07T04:53:38Z | |
| dc.description | 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 | |
| dc.description | 19 pages. To be published in: Commutative Algebra. Its interaction with Algebraic Geometry (Grenoble-Lyon 2001), Contemporary Math | |
| dc.identifier | https://arxiv.org/abs/math/0212125 | |
| dc.identifier | http://arxiv.org/abs/math/0212125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65932 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13C15; 13C25 (Primary), 18G15; 13D45 (Secondary) | |
| dc.title | Depth and amplitude for unbounded complexes | |
| dc.type | text |