Cohomological dimensions of specialization-closed subsets and subcategories of modules
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.05776
- arXiv:
- arXiv:1912.05776
- Bibcode:
- 2019arXiv191205776M
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Representation Theory;
- 13C60;
- 13D09;
- 13D45
- E-Print:
- 10 pages, to appear in PAMS