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arXiv · 1211.0945

Dualities in Koszul graded AS Gorenstein algebras

Roberto Martinez-Villa
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Abstract

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

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Roberto Martinez-Villa. 2012-11-05. Dualities in Koszul graded AS Gorenstein algebras. https://arxiv.org/abs/1211.0945

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