Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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.

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?

share|cite|improve this question
1 ? – Benjamin Dickman Sep 26 '12 at 6:45

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.