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arXiv · 1111.2902

The radius of a subcategory of modules

Hailong Dao·Ryo Takahashi
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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.

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Hailong Dao, Ryo Takahashi. 2013-09-23. The radius of a subcategory of modules. https://doi.org/10.2140/ant.2014.8.141

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