Classifying subcategories of modules over a commutative noetherian ring

• Autores: Ryo Takahashi
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 3, 2008, págs. 767-782
• Idioma: inglés
• DOI: 10.1112/jlms/jdn056
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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