The quot functor of a quasi-coherent sheaf
arXiv:1212.4544
Abstract
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.
v3 - 24 pages. Added several Remarks at the end of Sections 3 and 4.2. Some arguments clarified and expanded. 4 references added/updated. v4 - 25 pages. Few minor changes. To appear in the Asian J. Math