General Hilbert stacks and Quot schemes

Abstract

We prove the algebraicity of the Hilbert functor, the Hilbert stack, the Quot functor and the stack of coherent sheaves on an algebraic stack X with (quasi-)finite diagonal without any finiteness assumptions on X. We also give similar results for Hom stacks and Weil restrictions.

11 pages; corrected some minor errors; numbering changed in section 3; final version

References in corpus (2)

• The Hilbert Stack
• The quot functor of a quasi-coherent sheaf

Cited by in corpus (7)

• Coherent Tannaka duality and algebraicity of Hom-stacks
• A functorial formalism for quasi-coherent sheaves on a geometric stack
• Addendum: Étale dévissage, descent and pushouts of stacks
• Cohomology and base change for algebraic stacks
• The quot functor of a quasi-coherent sheaf
• Geometric Brauer residue via root stacks
• Rational Homotopy and Hodge Theory of Moduli Stacks of principal $G$-bundles