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Speaker: Sergey Arkhipov (Aarhus University)

Abstract:  This is a joint work in progress with Sebastian Orsted.  Given an algebraic variety X acted by an affine algebraic group G, we make sense of  the derived category of DG-modules over the DG-algebra of differential forms on X  equivariant with respect to differential forms on G. The construction uses an explicit model for  a certain homotopy limit of a diagram of  DG-categories developed in our earlier work and generalizing a recent result of Block, Holstein and Wei. We compare the obtained category with a certain category of sheaves on the (shifted) cotangent bundle T^*X descending to the Hamiltonian reduction of the cotangent bundle. Two special cases are of interest. In the first, X is a point. Thus we compare comodules over Omega(G)  with G-equivariant coherent sheaves on Lie(G). In the second case, X is a simple algebraic group, with the action of the square of the upper triangular subgroup. We obtain a category closely related to the affine Hecke category.

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