Open Collections

Cohomologically full rings

Banff International Research Station for Mathematical Innovation and Discovery

Inspired by a question raised by Eisenbud-Musta\c{t}\u{a}-Stillman regarding the injectivity of maps from Ext modules to local cohomology modules, we introduce a class of rings which we call cohomologically full rings. In positive characteristic, this notion coincides with that of F-full rings studied by Pham and Ma, while in characteristic $0$, they include Du Bois singularities. We prove many basic properties of cohomologically full rings, including their behavior under flat base change. We show that ideals defining these rings satisfy many desirable properties, in particular they have small cohomological and projective dimension. Furthermore, we obtain Kodaira-type vanishing and strong bounds on the regularity of cohomologically full graded algebras. Joint work with Alessandro De Stefani and Linquan Ma.

Mathematics; Commutative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: University of Kansas

2019-03-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69094

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/