Algebra/Topology seminar

Speaker: Sebastian Ørsted

Title: Equivariant sheaves on loop spaces

Abstract: We present recent work relating the derived category of derived Hamiltonian reduction of the cotangent bundle T^*X of a scheme X with respect to the action of an affine group scheme G to the derived category of the loop space LX, equivariant with respect to the action of the loop group LG.
After decomposing
LG = ( based loops at e ∈ G ) ⋊ G
and consequently imposing LG-equivariance in two steps, the statement boils down to an exotic notion of Koszul duality where the base is a dg-algebra rather than a commutative ring.
The purpose of the work is to analyze the affine Hecke category by rewriting it as a category of equivariant Ω_G-modules.