Vol. 286, No. 2, 2017

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Classifying resolving subcategories

William Sanders

Vol. 286 (2017), No. 2, 401–438
Abstract

We use the theory of Auslander–Buchweitz approximations to classify certain resolving subcategories containing a semidualizing or a dualizing module. In particular, we show that if the ring has a dualizing module, then the resolving subcategories containing maximal Cohen–Macaulay modules are in bijection with grade consistent functions and thus are the precisely the dominant resolving subcategories.

Keywords
resolving subcategory, homological dimension, commutative rings
Mathematical Subject Classification 2010
Primary: 13D05, 13C60
Secondary: 18G20, 13C14