Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771868 | Journal of Algebra | 2017 | 24 Pages |
Abstract
We examine local cohomology in the setting of valuation rings. The novelty of this investigation stems from the fact that valuation rings are usually non-Noetherian, whereas local cohomology has been extensively developed mostly in a Noetherian setting. Various vanishing results on local cohomology for valuation rings of finite Krull dimension are obtained, and a uniform bound on the global dimension of such rings is established. Our investigation reveals differences in the sheaf theoretic definition of local cohomology, and the algebraic definition in terms of a limit of certain Ext functors.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Rankeya Datta,