Stratifying triangulated categories

Abstract

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a classification of the localizing subcategories of T 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 T; and results concerning the support of the R-module of homomorphisms Hom_T^*(C,D) leading to an analogue of the tensor product theorem for support varieties of modular representation of groups.

25 pages; this version corrects some minor errors in the earlier one. This article has been accepted for publication in the Journal of Topology

References in corpus (1)

• Support varieties for selfinjective algebras

Cited by in corpus (30)

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• Homological support of big objects in tensor-triangulated categories
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• Duality for bounded derived categories of complete intersections
• A local-global principle for small triangulated categories
• Localizing subcategories in the Bootstrap category of separable C*-algebras
• Classification of resolving subcategories and grade consistent functions
• Affine weakly regular tensor triangulated categories
• The algebraic chromatic splitting conjecture for Noetherian ring spectra
• Stratifying derived categories of cochains on certain spaces
• Duality pairs, phantom maps, and definability in triangulated categories
• High Frobenius pushforwards generate the bounded derived category
• Variations of the telescope conjecture and Bousfield lattices for localized categories of spectra
• The Bousfield lattice of a triangulated category and stratification
• Colocalising subcategories of modules over finite group schemes
• Support theory for Drinfeld doubles of some infinitesimal group schemes
• Filtrations via tensor actions
• The relation between Grothendieck duality and Hochschild homology
• Filtrations in module categories, derived categories and prime spectra
• Cosupport for triangulated categories
• Matrix factorizations in higher codimension
• Homological stratification and descent
• Telescope conjecture via homological residue fields with applications to schemes
• Stratifying integral representations of finite groups
• Another version of cosupport for complexes