Cohomological dimensions of specialization-closed subsets and subcategories of modules
Commutative Algebra
2020-09-28 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1912.05776,
title = {Cohomological dimensions of specialization-closed subsets and subcategories of modules},
author = {Hiroki Matsui and Tran Tuan Nam and Ryo Takahashi and Nguyen Minh Tri and Do Ngoc Yen},
journal= {arXiv preprint arXiv:1912.05776},
year = {2020}
}
Comments
10 pages, to appear in PAMS