Stratifying Triangulated Categories
نویسنده
چکیده
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 graded R-module of morphisms HomT(C,D) leading to analogues of the tensor product theorem for support varieties of modular representation of groups.
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