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Abstract
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Let R be a commutative
noetherian local ring, and let X be a resolving subcategory of the category of finitely
generated R-modules. In this paper, we study modules in X by relating them to
modules in X which are free on the punctured spectrum of R. We do this by
investigating nonfree loci and establishing an analogue of the notion of a level in a
triangulated category which has been introduced by Avramov, Buchweitz, Iyengar
and Miller. As an application, we prove a result on the dimension of the nonfree
locus of a resolving subcategory having only countably many nonisomorphic
indecomposable modules in it, which is a generalization of a theorem of Huneke and
Leuschke.
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Keywords
resolving subcategory, resolving closure,
nonfree locus, Cohen–Macaulay ring, maximal
Cohen–Macaulay module, countable Cohen–Macaulay
representation type, totally reflexive module
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Mathematical Subject Classification
Primary: 13C05, 16D90, 16G60, 16G50,
13C14, 13C13
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Milestones
Received: 15 August 2008
Revised: 28 December 2008
Accepted: 19 December 2008
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