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We give a variant of Artin algebraization along closed subschemes and closedsubstacks. Our main application is the existence of \'etale, smooth, orsyntomic neighborhoods of closed subschemes and closed substacks. Inparticular, we prove local structure theorems for stacks and their derivedcounterparts and the existence of henselizations along linearly fundamentalclosed substacks. These results establish the existence of Ferrand pushouts,which answers positively a question of Temkin-Tyomkin.

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