The radius of a subcategory of modules

Abstract

We introduce a new invariant for subcategories X of finitely generated modules over a local ring R which we call the radius of X. We show that if R is a complete intersection and X is resolving, then finiteness of the radius forces X to contain only maximal Cohen-Macaulay modules. We also show that the category of maximal Cohen-Macaulay modules has finite radius when R is a Cohen-Macaulay complete local ring with perfect coefficient field. We link the radius to many well-studied notions such as the dimension of the stable category of maximal Cohen-Macaulay modules, finite/countable Cohen-Macaulay representation type and the uniform Auslander condition.

Final version, to appear in Algebra and Number Theory

References in corpus (4)

• Asymptotic behavior of Tor over complete intersections and applications
• Duality for bounded derived categories of complete intersections
• The dimension of a subcategory of modules
• Classification of resolving subcategories and grade consistent functions

Cited by in corpus (20)

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• Annihilation of cohomology and strong generation of module categories
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• On reducing homological dimensions over noetherian rings
• Auslander-Reiten annihilators
• Building modules from the singular locus
• Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi
• Singular equivalences of commutative noetherian rings and reconstruction of singular loci
• Remarks on dimensions of triangulated categories
• On the Subcategories of n-Torsionfree Modules and Related Modules
• Comparisons between Annihilators of Tor and Ext
• Generation in singularity categories of hypersurfaces of countable representation type
• On the radius of the category of extensions of matrix factorizations
• Reflexive modules, self-dual modules and Arf rings