Local cohomology and support for triangulated categories
Local cohomology and support for triangulated categories
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DOI：
10.24033/asens.2076
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发表时间：
2007-02
影响因子：
1.9
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
我们提出了一种新的方法来定义在任何允许小余积的紧致生成的三角范畴中的对象的支持度的概念。这种方法是基于三角范畴上关于中心算子环的局部上同调函数的构造。适当的专门化可以恢复Foxby和Neeman的交换Notherian环的理论，完全交局部环的Avramov和Buch-Weitz理论，以及根据Benson，Carlson和Rickard的有限群表示的变体。我们给出了三角支集和上同调支集不同的对象的显式例子。在群表示的情况下，这允许我们纠正和建立Benson猜想。
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small co- products. This approach is based on a construction of local cohomology func- tors on triangulated categories, with respect to a central ring of operators. Suitably specialized one recovers, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buch- weitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects whose triangulated support and cohomological support dif- fer. In the case of group representations, this allows us to correct and establish a conjecture of Benson.