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.
Cite
@article{arxiv.0910.0642,
title = {Stratifying triangulated categories},
author = {Dave Benson and Srikanth B. Iyengar and Henning Krause},
journal= {arXiv preprint arXiv:0910.0642},
year = {2014}
}
Comments
25 pages; this version corrects some minor errors in the earlier one. This article has been accepted for publication in the Journal of Topology