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

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

doi:10.1017/fms.2023.60

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 journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Article number	e20
Journal	Forum of Mathematics, Sigma
Volume	12
DOIs	https://doi.org/10.1017/fms.2023.60
State	Published - Feb 1 2024
Externally published	Yes

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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10.1017/fms.2023.60

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abstract = "We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of {\'e}tale, 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.",

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AU - Alper, Jarod

AU - Hall, Jack

AU - Halpern-Leistner, Daniel

AU - Rydh, David

PY - 2024/2/1

Y1 - 2024/2/1

N2 - 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.

AB - 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.

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JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e20

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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