Cohomological dimensions of specialization-closed subsets and subcategories of modules
Copyright policy )Cohomological dimensions of specialization-closed subsets and subcategories of modules
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.
10 pages, to appear in PAMS
- Nagoya University Japan
- University of the Sciences United States
- Dong A University Viet Nam
- University of Tokyo Japan
- Tokai National Higher Education and Research System Japan
13C60, 13D09, 13D45, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Mathematics - Representation Theory
13C60, 13D09, 13D45, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Mathematics - Representation Theory
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