Classifying KE-closed subcategories over a commutative noetherian ring

2025/09/06 by Toshinori Kobayashi, Kobayashi, Toshinori, Shunya Saito +1
Mathematics · #Rings, Modules, and Algebras #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2509.05767

Abstract

Let mod R denote the category of finitely generated R-modules for a commutative noetherian ring R. In this paper, we investigate KE-closed subcategories of mod R as a continuation of our previous work. We associate a function on Spec R with each KE-closed subcategory of mod R, and show that this function completely determines the original subcategory. To classify the functions obtained from KE-closed subcategories, we introduce the notion of an n-Bass function for each n≥ 0. We obtain a bijection between the set of KE-closed subcategories and the set of 2-Bass functions provided that R is (S₂)-excellent in the sense of Česnavičius.

Citations

• When are KE-closed subcategories torsion-free classes?
• IE-closed subcategories of commutative rings are torsion-free classes
• Image-extension-closed subcategories of module categories of hereditary algebras
• Faltings' annihilator theorem and t-structures of derived categories
• Classifying subcategories of modules over Noetherian algebras
• Classification of resolving subcategories and grade consistent functions
• Exact Categories

Related

• When are KE-closed subcategories torsion-free classes?
• Classifying subcategories of modules
• Filtrations in module categories, derived categories and prime spectra
• Classification of resolving subcategories and grade consistent functions
• Classifying preaisles of derived categories of complete intersections