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Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts
Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA, Box 354350.
School of Mathematics & Statistics, The University of Melbourne, Parkville, VIC 3010, Australia.
Department of Mathematics, Cornell University, 310 Mallot Hall, Ithaca, NY 14853, USA, 310 Mallot Hall.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2505-6417
2024 (English)In: Forum of Mathematics, Sigma, E-ISSN 2050-5094, Vol. 12, article id e20Article in journal (Refereed) Published
Abstract [en]

We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of ├ętale, 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.

Place, publisher, year, edition, pages
Cambridge University Press (CUP) , 2024. Vol. 12, article id e20
Keywords [en]
14B12 14D23
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-344005DOI: 10.1017/fms.2023.60ISI: 001153360600001Scopus ID: 2-s2.0-85185289560OAI: oai:DiVA.org:kth-344005DiVA, id: diva2:1841375
Note

QC 20240301

Available from: 2024-02-28 Created: 2024-02-28 Last updated: 2024-03-01Bibliographically approved

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Rydh, David

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