Derived Quot schemes (Q2730735)

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.