Depth for triangulated categories (Q2812600)
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scientific article; zbMATH DE number 6594586
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Depth for triangulated categories |
scientific article; zbMATH DE number 6594586 |
Statements
17 June 2016
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triangulated category
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depth
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dimension
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local cohomology
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Depth for triangulated categories (English)
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Let \(\mathcal T\) be a compactly generated triangulated category having small coproducts. For such a \(\mathcal T\), \textit{D. Benson} et al. defined in [Ann. Sci. Éc. Norm. Supér. (4) 41, No. 4, 575--621 (2008; Zbl 1171.18007)], local cohomology functors. Using their ideas, the authors of the paper under review introduce the depth of objects in \(\mathcal T\). It is proved that when \((R,\mathfrak{m})\) is a graded commutative Noetherian local ring, then the depth of any cohomologically bounded and cohomologically finite object is not larger than its dimension.
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