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arXiv · 1912.05776

Cohomological dimensions of specialization-closed subsets and subcategories of modules

Hiroki Matsui·Tran Tuan Nam·Ryo Takahashi·Nguyen Minh Tri·Do Ngoc Yen
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Abstract

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.

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Hiroki Matsui, Tran Tuan Nam, Ryo Takahashi, Nguyen Minh Tri, Do Ngoc Yen. 2019-12-12. Cohomological dimensions of specialization-closed subsets and subcategories of modules. https://arxiv.org/abs/1912.05776

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