Classifying Serre subcategories via atom spectrum

DOI10.1016/J.AIM.2012.07.009zbMath1255.18011arXiv1112.6253OpenAlexW1995144747MaRDI QIDQ456769

Ryo Kanda

Publication date: 16 October 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.6253

zbMATH Keywords

localizing subcategorySerre subcategoryatom spectrummonoform objectZiegler spectrum

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10)

Related Items (20)

Coserreness with respect to specialization closed subsets and some Serre subcategories ⋮ A classification of some thick subcategories in locally noetherian Grothendieck categories ⋮ Melkersson condition for extension of Serre subcategories ⋮ Support theory of abelian categories -- some discussion ⋮ HEREDITARY TORSION THEORIES OF A LOCALLY NOETHERIAN GROTHENDIECK CATEGORY ⋮ Local cohomology in Grothendieck categories ⋮ Structural theorem for gr-injective modules over gr-noetherian G-graded commutative rings and local cohomology functors ⋮ Extension groups between atoms and objects in locally noetherian Grothendieck category ⋮ Finiteness of the number of minimal atoms in Grothendieck categories ⋮ A classification of torsion classes in abelian categories ⋮ Cohomological dimensions of specialization-closed subsets and subcategories of modules ⋮ Monoform objects and localization theory in abelian categories ⋮ Extension groups between atoms in abelian categories ⋮ Injective spectra and torsion theories ⋮ Integrality of Noetherian Grothendieck categories ⋮ Attached atoms in Grothendieck categories ⋮ Atom spectra of graded rings and sheafification in toric geometry ⋮ Construction of Grothendieck categories with enough compressible objects using colored quivers ⋮ Non-exactness of direct products of quasi-coherent sheaves ⋮ Specialization orders on atom spectra of Grothendieck categories

Cites Work

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• A ONE-SIDED PRIME IDEAL PRINCIPLE FOR NONCOMMUTATIVE RINGS
• Classifying subcategories of modules over a commutative noetherian ring
• The Ziegler Spectrum of a Locally Coherent Grothendieck Category
• Classifying Serre subcategories of finitely presented modules
• Rank theory of modules
• Des catégories abéliennes

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