Linear Koszul duality

Simon Riche (1) , Ivan Mirkovic (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 UMass Amherst - University of Massachusetts [Amherst]

In this paper we construct, for F_1 and F_2 subbundles of a vector bundle E, a ``Koszul duality'' equivalence between derived categories of \Gm-equivariant coherent (dg-)sheaves on the derived intersection of F_1 and F_2 inside E, and the corresponding derived intersection of orthogonals in the dual vector space. We also propose applications to Hecke algebras.

Domaines: Théorie des représentations [math.RT]

Simon Riche, Ivan Mirkovic. Linear Koszul duality. Compositio Mathematica, 2010, 146, pp.233-258. ⟨hal-00476254⟩