The radius of a subcategory of modules

Details The radius of a subcategory of modules The radius of a subcategory of modules

2011-11-12

arxiv.org/abs/1111.2902v2

Mathematics

Commutative Algebra

Scientific paper

We introduce a new invariant for a subcategory 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 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, the uniform Auslander condition and the syzygetic Artin-Rees condition.

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