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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/9941

Title: Homology of Perfect Complexes
Authors: Buchweitz, Ragnar-Olaf
Avramov, Luchezar l.
Iyengar, Srikanth
Miller, Claudia
Keywords: Homology
Perfect Complexes
New Intersection Theorem
Lowey Length
Triangulated Category
Issue Date: 2006
Citation: 2000 Mathematics Subject Classification. 13D05, 13H10, 13D40; 13B10, 13D07, 13D25, 18E30.
Abstract: It is proved that the sum of the Loewy length of the homology modules of a finite free complex F over a local ring R is bounded below by an invariant that measures the singularity of R. In the special case of the group algebra of an elementary abelian group one recovers results of G. Carlsson and of C. Allday and V. Puppe. The arguments use numerical invariants of objects in general triangulated categories, introduced in the paper and called levels. One such level models projective dimension; a lower bound for this level contains the New Intersection Theorem for commutative local rings containing fields. The lower bound on Loewy length of the homology of F is sharp in general. Under additional hypothesis on the ring R stronger estimates are proved for Loewy lengths of modules of finite projective dimension.
Description: http://arXiv.org/abs/math.AC/0609008 v1 31 Aug 2006
URI: http://hdl.handle.net/1807/9941
Appears in Collections:Mathematics

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