Stratifying triangulated categories
Stratifying triangulated categories
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DOI：
10.1112/jtopol/jtr017
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发表时间：
2009-10
影响因子：
1.1
通讯作者：
D. Benson;S. Iyengar;H. Krause
中科院分区：
文献类型：
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作者：
D. Benson;S. Iyengar;H. Krause
对于任何紧生成的三角化范畴，即被赋予了一个分级交换诺瑟环R的作用的范畴，引入了分层的概念。这个概念的效用是通过建立各种结果来证明的，这些结果是：如果一个范畴被R分层，其中包括一个范畴的局部化子范畴在R中的素理想集合的子集上的分类；紧对象的子范畴的粗子范畴的分类以及关于态射的梯度R -模的支持的结果hm *∞(C， D)，导致了群的模表示的支持变体的张量积定理的类似。
A notion of stratification is introduced for any compactly generated triangulated category ⊤ endowed with an action of a graded‐commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences that follow if ⊤ is stratified by R. Among them are a classification of the localizing subcategories of ⊤ 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 ⊤; and results on the support of the graded R‐module of morphisms Hom*⊤(C, D) leading to analogs of the tensor product theorem for support varieties of modular representation of groups.