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Derived Quot schemes. (English) Zbl 1050.14042
A derived version of Grothendieck’s Quot scheme is constructed. Let \(X\) be a projective scheme over a field \(\mathbb{K}\) and \({\mathcal F}\) a fixed coherent sheaf on \(X\). We take a \(h'\in\mathbb{Q}[t]\) and put \(h= h^{{\mathcal F}}- h'\) in which \(h^{{\mathcal F}}\) is the Hilbert polynomial of \({\mathcal F}\). Informally, the Quot scheme can be thought of as a Grassmannian of subsheaves in \({\mathcal F}\); its closed points are in 1:1 correspondence with \(\text{Sub}_h({\mathcal F})= \{{\mathcal K}\subset{\mathcal F}: h^{{\mathcal F}}= h\}\). In the same situation, the authors construct a dg-manifold \(\text{RSub}_h({\mathcal F})\) as a graded version of the derived Grassmannian.

MSC:
14M17 Homogeneous spaces and generalizations
18E30 Derived categories, triangulated categories (MSC2010)
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