对的阿尔丁代数化及其在堆栈局部结构和费朗推出中的应用

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2024-02-01 DOI:10.1017/fms.2023.60

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

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引用次数: 0

摘要

我们给出了沿着封闭子方案和封闭子包的阿尔丁代数化变体。我们的主要应用是封闭子方案和封闭子栈的étale、光滑或合成邻域的存在。特别是，我们证明了堆栈及其派生对应物的局部结构定理，以及沿着线性基本封闭子堆栈的henselizations的存在性。这些结果确立了费朗推演的存在性，正面回答了特姆金-焦姆金的一个问题。

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

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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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.