Representability of Hilbert schemes and Hilbert stacks of points

Abstract

We show that the Hilbert functor of points on an arbitrary separated algebraic stack is an algebraic space. We also show the algebraicity of the Hilbert stack of points on an algebraic stack and the algebraicity of the Weil restriction of an algebraic stack along a finite flat morphism. For the latter two results, no separation assumptions are necessary.

15 pages; major revision, final version

References in corpus (2)

• Artin's axioms, composition and moduli spaces
• Simultaneous normalization and algebra husks

Cited by in corpus (14)

• Noetherian approximation of algebraic spaces and stacks
• Existence and properties of geometric quotients
• Étale dévissage, descent and pushouts of stacks
• Coherent Tannaka duality and algebraicity of Hom-stacks
• The Hilbert Stack
• General Hilbert stacks and Quot schemes
• The Balmer spectrum of a tame stack
• Families of zero cycles and divided powers: I. Representability
• Moduli spaces of hyperelliptic curves with A and D singularities
• Stringy invariants and toric Artin stacks
• Addendum: Étale dévissage, descent and pushouts of stacks
• A motivic change of variables formula for Artin stacks
• An inclusion-exclusion principle for tautological sheaves on Hilbert schemes of points
• The plectic conjecture over local fields