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arXiv · 0910.0642

Stratifying triangulated categories

Dave Benson·Srikanth B. Iyengar·Henning Krause
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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.

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Dave Benson, Srikanth B. Iyengar, Henning Krause. 2011-05-13. Stratifying triangulated categories. https://doi.org/10.1112/jtopol%2Fjtr017

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