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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 R. The utility of this notion is demonstrated by establishing diverse consequences that follow if is stratified by R. Among them are a classification of the localizing subcategories of in terms of subsets of the set of prime ideals in R; a classification of the thick subcategories of the subcategory of compact objects in ; and results on the support of the graded R-module of morphisms Hom*(C, D) leading to analogs of the tensor product theorem for support varieties of modular representation of groups.
- Subjects
NOETHERIAN rings; ASSOCIATIVE rings; COMMUTATIVE rings; HOMOLOGY theory; OPERATIONS (Algebraic topology)
- Publication
Journal of Topology, 2011, Vol 4, Issue 3, p641
- ISSN
1753-8416
- Publication type
Article
- DOI
10.1112/jtopol/jtr017