Gennaro Di Brino: Quot functors for quasi-coherent sheaves on projective schemes

In his fundamental work on Hilbert schemes, Grothendieck proves the existence of a projective scheme parametrizing quotients of a \emph{coherent} sheaf over a projective base scheme. We will show that one can push the above construction further and obtain an infinite dimensional scheme parametrizing quotients of a \emph{quasi-coherent} sheaf on a projective scheme. We will achieve this via a sharpening of Grothendieck's Grassmannian embedding due to Ciocan-Fontanine and Kapranov combined with a result of Deligne, realizing quasi-coherent sheaves as ind-objects in the category of quasi-coherent sheaves of finite presentation. Finally, we will briefly compare our result with the recent work of R. Skjelnes.