The \textit{quot} functor of a quasi-coherent sheaf
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Publication:1741599
DOI10.4310/AJM.2019.V23.N1.A1zbMATH Open1410.14006arXiv1212.4544OpenAlexW2943681491MaRDI QIDQ1741599
Publication date: 6 May 2019
Published in: The Asian Journal of Mathematics (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1212.4544
Grassmannians, Schubert varieties, flag manifolds (14M15) Parametrization (Chow and Hilbert schemes) (14C05) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20)
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