Stratifying triangulated categories
A notion of stratification is introduced for any compactly generatedtriangulated category T endowed with an action of a graded commutativenoetherian ring R. The utility of this notion is demonstrated by establishingdiverse consequences which follow when T is stratified by R. Among them are aclassification of the localizing subcategories of T in terms of subsets of theset of prime ideals in R; a classification of the thick subcategories of thesubcategory of compact objects in T; and results concerning the support of theR-module of homomorphisms Hom_T^*(C,D) leading to an analogue of the tensorproduct theorem for support varieties of modular representation of groups.
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Oxford Univ. Press