Classifying subcategories of modules over a commutative noetherian ring

By Ryo Takahashi. 2008

55 citations recorded by the source corpus.

Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal. Hovey gave a bijection between the set of coherent subcategories of the category of finitely presented R‐modules and the set of thick subcategories of the derived category of perfect R‐complexes. Using this bijection, he proved that every coherent subcategory of finitely presented R‐modules is a Serre subcategory. In this paper, it is proved that this holds whenever R is a commutative noetherian ring. This paper also yields a module version of the bijection between the set of localizing subcategories of the derived category of R‐modules and the set of subsets of Spec R which was given by Neeman.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7950f941e0f2837a114bf8c25032c37f545efa9e

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Classifying thick subcategories of the stable category of Cohen-Macaulay modules (2009, background): “A lot of analogous classification results of subcategories of modules have been obtained by many authors; see [35, 51, 44, 25, 26, 27] for instance.”
Classification of resolving subcategories and grade consistent functions (2012, result): “For many other similar results, see [5, 17, 19, 21, 23] and the references therein.”
Classifying Serre subcategories via atom spectrum (2011, background): “Classification of localizing subcategories and Serre subcategories is quite an active subject widely studied by a number of authors (see, for example, [3,5,6,11], and [1]).”
Thick subcategories of modules over commutative noetherian rings (with an appendix by Srikanth Iyengar) (2008, background): “More recently, a number of authors studied subcategories of ModA in terms of subsets of Spec A; see [9, 11, 16].”