The $\mathit{Quot}$ functor of a quasi-coherent sheaf

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.

Keywords

$\mathit{Quot}$ scheme, quasi-coherent sheaf, sheaf of finite presentation, Grassmannian embedding

2010 Mathematics Subject Classification

Primary 14C05. Secondary 14M15, 18F20.

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Received 12 March 2017

Accepted 11 May 2017

Published 3 May 2019