(Non)Vanishing results on local cohomology of valuation rings
arXiv:1601.01954 · doi:10.1016/j.jalgebra.2016.12.032
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. We prove various vanishing results on local cohomology for valuation rings of finite Krull dimension. These vanishing results stem from a uniform bound on the global dimension of such rings. 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.
Comments are welcome; latest edit corrects numerous typos and makes the article consistent with the journal version