Classification of resolving subcategories and grade consistent functions

Abstract

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.

Some minor changes from the referees' suggestions. To appear in International Mathematics Research Notices

References in corpus (3)

• The radius of a subcategory of modules
• Tilting, cotilting, and spectra of commutative noetherian rings
• The dimension of a subcategory of modules

Cited by in corpus (5)

• The radius of a subcategory of modules
• Tilting, cotilting, and spectra of commutative noetherian rings
• Local rings with quasi-decomposable maximal ideal
• Classifying Resolving Subcategories
• Colocalization and cotilting for commutative noetherian rings