(Non)Vanishing results on local cohomology of valuation rings

JOURNAL OF ALGEBRA

卷:479

Article

Datta, Rankeya¹ 

[1] Univ Michigan, Dept Math, 2074 East Hall,530 Church St, Ann Arbor, MI 48109 USA

关键词: Valuation rings;    Local cohomology;   

DOI  :  10.1016/j.jalgebra.2016.12.032

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free