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Linear Koszul duality

Part of: Homological methods Rings and algebras arising under various constructions Abelian categories

Published online by Cambridge University Press:  16 December 2009

Ivan Mirković  and
Simon Riche
Ivan Mirković
Affiliation:
University of Massachusetts, Amherst, MA, USA (email: [email protected])
Simon Riche
Affiliation:
Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu (UMR 7586 du CNRS), Équipe d’Analyse Algébrique, 175, rue du Chevaleret, 75013 Paris, France (email: [email protected])
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Abstract

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In this paper we construct, for F1 and F2 subbundles of a vector bundle E, a ‘Koszul duality’ equivalence between derived categories of 𝔾m-equivariant coherent(dg-)sheaves on the derived intersection , and the corresponding derived intersection . We also propose applications to Hecke algebras.

Keywords

dg-schemessheaves of dg-algebrasderived intersectionKoszul duality

MSC classification

Secondary: 18E30: Derived categories, triangulated categories 16E45: Differential graded algebras and applications 16S37: Quadratic and Koszul algebras
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 1 , January 2010 , pp. 233 - 258
Copyright
Copyright © Foundation Compositio Mathematica 2009

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