Cohomological dimensions of specialization-closed subsets and subcategories of modules
Cohomological dimensions of specialization-closed subsets and subcategories of modules
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DOI：
10.1090/proc/15102
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发表时间：
2019-12
影响因子：
1
通讯作者：
H. Matsui;T. Nam;Ryo Takahashi;N. Tri;D. N. Yen
中科院分区：
文献类型：
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作者：
H. Matsui;T. Nam;Ryo Takahashi;N. Tri;D. N. Yen
设R是交换Noether环.本文研究Spec R的特化闭子集。更准确地说，我们首先刻画的专业化闭子集的各种封闭性质的子范畴的模块。然后，对于每个非负整数n，我们引入了n-宽的R-模的子范畴的概念，考虑的问题问，当一个给定的专门化闭子集的上同调维数最多为n。
Let R be a commutative noetherian ring. In this paper, we study specialization-closed subsets of Spec R. More precisely, we first characterize the specialization-closed subsets in terms of various closure properties of subcategories of modules. Then, for each nonnegative integer n we introduce the notion of n-wide subcategories of R-modules to consider the question asking when a given specialization-closed subset has cohomological dimension at most n.