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We classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring  R  by using integer-valued functions on  Spec  R . As an application, we give a complete classification of resolving subcategories when  R  is a locally hypersurface ring or a complete intersection. Our results also recover and categorify a “missing theorem” by Auslander.

Classification of Resolving Subcategories and Grade Consistent Functions