The quot functor of a quasi-coherent sheaf

2012/12/19 by Di Brino, Gennaro
#14A15 #14C05 #14M15 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/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.

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