Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts
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2024-02-01
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Forum of Mathematics, Sigma
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CAMBRIDGE UNIV PRESS
Melbourne Authors
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School of Mathematics and Statistics
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Journal Article
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Alper, J., Hall, J., Halpern-Leistner, D. & Rydh, D. (2024). Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts. Forum of Mathematics Sigma, 12, https://doi.org/10.1017/fms.2023.60.
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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.