Equivariant sheaves on loop spaces

Sergey Arkhipov; Sebastian Ørsted

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arXiv · 2008.04794

Equivariant sheaves on loop spaces

Sergey Arkhipov·Sebastian Ørsted

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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 $Ω_X$ on $X$ equivariant with respect to the action of a derived group scheme $(G ,Ω_G )$. 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 $T^* X$.

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BibTeX RIS

Sergey Arkhipov, Sebastian Ørsted. 2023-02-02. Equivariant sheaves on loop spaces. https://arxiv.org/abs/2008.04794

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