The Hilbert stack

Jack Hall; David Rydh

doi:10.1016/j.aim.2013.12.002

The Hilbert stack

Jack Hall^*, David Rydh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Let π : X → S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack-the Hilbert stack-parameterizing proper algebraic stacks mapping quasi-finitely to X. This was previously unknown, even for a morphism of schemes.

Original language	English
Pages (from-to)	194-233
Number of pages	40
Journal	Advances in Mathematics
Volume	253
DOIs	https://doi.org/10.1016/j.aim.2013.12.002
Publication status	Published - 1 Mar 2014

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10.1016/j.aim.2013.12.002

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title = "The Hilbert stack",

abstract = "Let π : X → S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack-the Hilbert stack-parameterizing proper algebraic stacks mapping quasi-finitely to X. This was previously unknown, even for a morphism of schemes.",

keywords = "Generalized Stein factorizations, Hilbert stack, Non-separated, Pushouts",

author = "Jack Hall and David Rydh",

year = "2014",

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AU - Hall, Jack

AU - Rydh, David

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N2 - Let π : X → S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack-the Hilbert stack-parameterizing proper algebraic stacks mapping quasi-finitely to X. This was previously unknown, even for a morphism of schemes.

AB - Let π : X → S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack-the Hilbert stack-parameterizing proper algebraic stacks mapping quasi-finitely to X. This was previously unknown, even for a morphism of schemes.

KW - Generalized Stein factorizations

KW - Hilbert stack

KW - Non-separated

KW - Pushouts

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U2 - 10.1016/j.aim.2013.12.002

DO - 10.1016/j.aim.2013.12.002

M3 - Article

SN - 0001-8708

VL - 253

SP - 194

EP - 233

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The Hilbert stack

Abstract

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