Geodesic
Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts
Forum of Mathematics, Sigma, Tome 12 (2024)

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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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     author = {Jarod Alper and Jack Hall and Daniel Halpern-Leistner and David Rydh},
     title = {Artin algebraization for pairs with applications to the local structure of stacks and {Ferrand} pushouts},
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Jarod Alper; Jack Hall; Daniel Halpern-Leistner; David Rydh. Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2023.60

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