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 noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.
Cite
@article{arxiv.math/0602344,
title = {Class and rank of differential modules},
author = {Luchezar L. Avramov and Ragnar-Olaf Buchweitz and Srikanth Iyengar},
journal= {arXiv preprint arXiv:math/0602344},
year = {2009}
}
Comments
27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematicae