 
Summary: HOMOLOGY OF PERFECT COMPLEXES
LUCHEZAR L. AVRAMOV, RAGNAROLAF BUCHWEITZ,
SRIKANTH IYENGAR, AND CLAUDIA MILLER
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.
Contents
Introduction 2
1. Loewy length of modules of finite projective dimension 5
2. Levels in triangulated categories 8
3. Levels of DG modules 11
4. Perfect DG modules 15
