Koszul duality and equivalences of categories

Fløystad, Gunnar

doi:10.1090/S0002-9947-05-04035-3

Koszul duality and equivalences of categories
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by Gunnar Fløystad PDF

Trans. Amer. Math. Soc. 358 (2006), 2373-2398 Request permission

Abstract:

Let $A$ and $A^{!}$ be dual Koszul algebras. By Positselski a filtered algebra $U$ with $\text {gr} U = A$ is Koszul dual to a differential graded algebra $(A^{!},d)$. We relate the module categories of this dual pair by a $\otimes -\text {Hom}$ adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg, and Soergel.

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