Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts

Jarod Alper, Jack Hall, Daniel Halpern-Leistner, David Rydh

Research output: Contribution to journalArticlepeer-review

Abstract

We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of étale, smooth or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove local structure theorems for stacks and their derived counterparts and the existence of henselizations along linearly fundamental closed substacks. These results establish the existence of Ferrand pushouts, which answers positively a question of Temkin-Tyomkin.

Original languageEnglish (US)
Article numbere20
JournalForum of Mathematics, Sigma
Volume12
DOIs
StatePublished - Feb 1 2024
Externally publishedYes

Keywords

  • 14B12 14D23

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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