Class rank of differential modules
type: Item
instance of: scholarly article
title: Class rank of differential modules
zbMATH Open document ID: 1153.13010
author: Luchezar L. Avramov
author: Ragnar-Olaf Buchweitz
author: Srikanth B. Iyengar
published in: Inventiones Mathematicae
publication date: 2008-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0602344
review text: A differential flag of a differential module is a bounded below filtration such that the differential maps every level of the filtration into the level below. The projective class of a differential module is the smallest length of a differential filtration with projective factors. One can similarly define other classes based on other types of modules. The main result is the class inequality (Corollary 4.2), stating that over commutative noetherian rings with big Cohen-Macaulay modules, a lower bound for the projective class of a finitely generated differential module is the super height of the annihilator of the homology of any of its retract. (The super height is the supremum of heights of the ideal over all commutative noetherian base changes.) As an application, a lower bound is obtained for the rank of finitely generated differential modules with free differential flag over commutative noetherian rings as the double of the annihilator of the super height of the annihilator of the homology of any of its retract.
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13D05
zbMATH DE Number: 5353176
zbMATH Keywords: projective class of differential modules
zbMATH Keywords: class inequality
zbMATH Keywords: finitely generated modules over a commutative noetherian ring
zbMATH Keywords: homological algebra of differential modules
MaRDI profile type: Publication
OpenAlex ID: W3104788913
arXiv ID: math/0602344
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DOI: 10.1007/S00222-007-0041-6
description: scientific article