Classification of resolving subcategories and grade consistent functions

2012/02/25 by Hailong Dao, Ryo Takahashi, Dao, Hailong +1 · 4 citations
Mathematics · #13C60 (Primary) 13D05 #13H10 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AC #math.CT #math.RA #math.RT #msc:13C60 #msc:13D05 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1202.5605

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

openalex publication_date 2012/02/25 · arxiv created 2013/06/14 · arxiv updated 2013/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Classifying KE-closed subcategories over a commutative noetherian ring
• When are syzygies of the residue field self-dual?
• On the depth of tensor products over Cohen-Macaulay rings
• Tilting, cotilting, and spectra of commutative noetherian rings

Related

• Modules in resolving subcategories which are free on the punctured spectrum
• Classifying resolving subcategories over a Cohen-Macaulay local ring
• On the finiteness of radii of resolving subcategories
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• Contravariantly finite resolving subcategories over commutative rings