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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?

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arxiv.org/abs/0808.0407 ? –  Benjamin Dickman Sep 26 '12 at 6:45

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