Dualities in Koszul graded AS Gorenstein algebras

Abstract

The paper is dedicated to the study of certain non commutative graded AS Gorenstein algebras $\Lambda$. The main result of the paper is that for Koszul algebras $\Lambda$ with Yoneda algebra $\Gamma$, such that both $\Lambda$ and $\Gamma$ are graded AS Gorenstein noetherian of finite local cohomology dimension on both sides, there are dualities of triangulated categories: \underline{$gr$}${}_{\Lambda }[{\Omega }^{-1}]$ $\cong D^b(Qg{r}_{\Gamma })$ and \underline{$gr$}${}_{\Gamma }[{\Omega }^{-1}]$ $\cong D^b(Qg{r}_{\Lambda })$ where, and $Qg{r}_{\Gamma }$ is the category of tails, this is: the category of finitely generated graded modules $g{r}_{\Gamma }$ divided by the modules of finite length, and $D^b(Qg{r}_{\Gamma })$ the corresponding derived category and \underline{$gr$}${}_{\Lambda }[{\Omega }^{-1}]$ the stabilization of the category of finetely generated graded $\Lambda$-modules, module the finetely generated projective modules.