Classifying subcategories of modules over a commutative noetherian ring
Takahashi, Ryo
arXiv, 0808.0058 / Harvested from arXiv
Text on arXiv
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 isomorphism, 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.
Publié le : 2008-08-01
Classification:  Mathematics - Commutative Algebra,  Mathematics - Rings and Algebras,  13C05, 16D90, 18E30 
@article{0808.0058,
     author = {Takahashi, Ryo},
     title = {Classifying subcategories of modules over a commutative noetherian ring},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0808.0058}
}

Takahashi, Ryo. Classifying subcategories of modules over a commutative noetherian ring. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0808.0058/