2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78570Realizing a part of the Derived Deformation Theory program, we construct a "derived" analog of the Grothendieck's Quot scheme parametrizing subsheaves in a given coherent sheaf F on a smooth projective variety X. This analog is a differential graded manifold RQuot_h(F) (so it is always smooth in an appropriate sense) whose tangent space at a point represented by a subsheaf K in F, is a cochain complex quasiisomorphic to RHom(K, F/K).46 pages, AMS-TeX. Revised version, to appear in Ann. Sci. ENSAlgebraic Geometrytext