Equivariant sheaves on loop spaces

Abstract

Let $X$ be an affine, smooth, and Noetherian scheme over $\mathbb{C}$ acted on by an affine algebraic group $G$. Applying the technique developed in Arkhipov and Ørsted (2018a, 2018b), we define a dg-model for the derived category of dg-modules over the dg-algebra of differential forms ${\Omega }_X$ on $X$ equivariant with respect to the action of a derived group scheme $(G,{\Omega }_G)$. We compare the obtained dg-category with the one considered in Arkhipov and Kanstrup (2015) given by coherent sheaves on the derived Hamiltonian reduction of $T^{\ast }X$.

19 pages