{"title":"Equivariant sheaves on loop spaces","authors":"Sergey Arkhipov, Sebastian Ørsted","doi":"10.4310/mrl.2023.v30.n3.a2","DOIUrl":null,"url":null,"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 $\\href{https://doi.org/10.48550/arXiv.1807.03266}{[3, }\\href{ https://doi.org/10.48550/arXiv.1812.03583}{4]}$, 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 $\\href{https://doi.org/10.48550/arXiv.1510.07472}{[2]}$ given by coherent sheaves on the derived Hamiltonian reduction of $T^\\ast X$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"35 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n3.a2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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 $\href{https://doi.org/10.48550/arXiv.1807.03266}{[3, }\href{ https://doi.org/10.48550/arXiv.1812.03583}{4]}$, 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 $\href{https://doi.org/10.48550/arXiv.1510.07472}{[2]}$ given by coherent sheaves on the derived Hamiltonian reduction of $T^\ast X$.
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