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arXiv · 1212.4544

The quot functor of a quasi-coherent sheaf

Gennaro Di Brino
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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.

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Gennaro Di Brino. 2012-12-19. The quot functor of a quasi-coherent sheaf. https://arxiv.org/abs/1212.4544

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