User eric d - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T21:01:31Z http://mathoverflow.net/feeds/user/26788 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108112/noncommutative-castelnuovo-mumford-regularity Noncommutative Castelnuovo-Mumford regularity Eric D 2012-09-25T22:25:01Z 2012-09-25T22:25:01Z <p>I am looking for noncommutative version of Castelnuovo-Mumford regularity. To be more precise, let $A=\oplus_{i=0}^{\infty}A_{i}$ be a $good$ (finite global dimension, connected etc) noncommutative graded $\mathbb{C}$-algebra and $M=\oplus_{i=0}^{\infty}M_{i}$ a finitely generated graded right $A$-module. I would like to show that $$H^{i}(A,M(m-i))=0$$ for some $m \in \mathbb{N}$. Here $H^i(A,M)$ is left derived functor of $Hom(A,M)$ from quotient category $gr(A)/tor(A)$ to $\mathbb{C}$-vector space. </p> <p>I would like to know what condition on $A$ is required to have such vanishing of cohomology groups. Could anyone give me a reference for this? </p>