Authors: L. L. Avramov, R.-O. Buchweitz, S. Iyengar
Title: Class and rank of differential modules
Abstract:
A differential module is a module equipped with a square-zero
endomorphism.  This structure underpins complexes of modules over
rings, as well as differential graded modules over graded rings.
We establish lower bounds on the class---a substitute for the length
of a free complex---and on the rank of a differential module in terms
of invariants of its homology.  These results specialize to basic theorems
in commutative algebra and algebraic topology.  One instance
is a common generalization of the equicharacteristic case of the New
Intersection Theorem of Hochster, Peskine, P.  Roberts, and Szpiro,
concerning complexes over commutative noetherian rings, and of
a theorem of G.  Carlsson on differential graded modules over
graded polynomial rings.

Status: Invent. Math. (to appear)