Realizing 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).Comment: 46 pages, AMS-TeX. Revised version, to appear in Ann. Sci. EN
