The radius of a subcategory of modules

By Hailong Dao, Ryo Takahashi. 2011

61 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/e0114e27e50ce4295620c1fa49acbe6798745763

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Citations in the corpus

Classification of resolving subcategories and grade consistent functions (2012, background): “However, it has recently emerged that resolving categories of modR are reasonable objects to look at, and they capture substantial information on the singularities of R, see [9, 10].”
Annihilation of cohomology and strong generation of module categories (2014, background): “The arguments involve a construction of an ascending chain of subcategories built out of a single module, introduced by Dao and Takahashi [8].”