The Hilbert stack

Jack Hall, David Rydh

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish (US)
Pages (from-to)194-233
Number of pages40
JournalAdvances in Mathematics
StatePublished - Mar 1 2014


  • Generalized Stein factorizations
  • Hilbert stack
  • Non-separated
  • Pushouts

ASJC Scopus subject areas

  • Mathematics(all)


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