  We build an infinite dimensional scheme parametrizing isomorphism classes of
coherent quotients of a quasi-coherent sheaf on a projective scheme. The main
tool to achieve the construction is a version of Grothendieck's Grassmannian
embedding combined with a result of Deligne, realizing quasi-coherent sheaves
as ind-objects in the category of quasi-coherent sheaves of finite
presentation. We end our treatment with the discussion of a special case in
which we can retain an analog of the Grassmannian embedding.
