Classification of resolving subcategories and grade consistent functions

By Hailong Dao, Ryo Takahashi. 2012

49 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a2f98b609b49c95c3d02b61a5297b65a39825678

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In Algebra and Number Theory

1. Hailong Dao
2. Ryo Takahashi
3. D. White

In Geometry and Topology

1. Hailong Dao
2. Ryo Takahashi
3. D. White
4. Greg Stevenson

Citations in the corpus

• The radius of a subcategory of modules (2011, background): “This classification theorem is stated and proved in [13].”
• Tilting, cotilting, and spectra of commutative noetherian rings (2012, unknown): “R | AssM ⊆ Y }, established by Takahashi in [32, Theorem 4.1], between all subsets of Spec(R) and the subcategories of mod–”