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- Title
Stratifying triangulated categories.
- Authors
Benson, Dave; Iyengar, Srikanth B.; Krause, Henning
- Abstract
A notion of stratification is introduced for any compactly generated triangulated category ⊤ endowed with an action of a graded‐commutative noetherian ring <italic>R</italic>. The utility of this notion is demonstrated by establishing diverse consequences that follow if ⊤ is stratified by <italic>R</italic>. Among them are a classification of the localizing subcategories of ⊤ in terms of subsets of the set of prime ideals in <italic>R</italic>; a classification of the thick subcategories of the subcategory of compact objects in ⊤; and results on the support of the graded <italic>R</italic>‐module of morphisms Hom*⊤(<italic>C</italic>, <italic>D</italic>) leading to analogs of the tensor product theorem for support varieties of modular representation of groups.
- Subjects
RING theory; NOETHERIAN rings; COMMUTATIVE rings; GROUP theory; ABSTRACT algebra
- Publication
Journal of Topology, 2011, Vol 4, p641
- ISSN
1753-8416
- Publication type
Article
- DOI
10.1112/jtopol/jtr017