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Koszul duality and equivalences of categories


Author: Gunnar Fløystad
Journal: Trans. Amer. Math. Soc. 358 (2006), 2373-2398
MSC (2000): Primary 16S37, 16D90
DOI: https://doi.org/10.1090/S0002-9947-05-04035-3
Published electronically: December 20, 2005
MathSciNet review: 2204036
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Abstract: Let $ A$ and $ A^{!}$ be dual Koszul algebras. By Positselski a filtered algebra $ U$ with 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-$Hom adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg, and Soergel.


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Additional Information

Gunnar Fløystad
Affiliation: Matematisk Institutt, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway
Email: gunnar@mi.uib.no

DOI: https://doi.org/10.1090/S0002-9947-05-04035-3
Received by editor(s): January 26, 2004
Published electronically: December 20, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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