Classification of resolving subcategories and grade consistent functions
  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. Our results also recover a "missing theorem" by Auslander. 
Hailong Dao, Ryo Takahashi
math.AC math.CT math.RA math.RT