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摘要翻译：
我们发展了一个导出变形理论的框架，在所有特征中都有效。这给出了一个模型类别，协调了局部和全局方法的导出模理论。在特征0中，我们利用这一点证明了Kontsevich、Hinich和Manetti所考虑的DGLAs和SHLAs（L无穷代数）的同伦范畴是等价的，并且与Toen-Vezzosi和Lurie的派生栈是相容的。另一个应用是与任何经典变形问题（在任何特征上）相关的上同调群允许与Andre-Quillen上同调相同的运算。
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英文标题：
《Unifying derived deformation theories》
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作者：
J. P. Pridham
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最新提交年份：
2019
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We develop a framework for derived deformation theory, valid in all characteristics. This gives a model category reconciling local and global approaches to derived moduli theory. In characteristic 0, we use this to show that the homotopy categories of DGLAs and SHLAs (L infinity algebras) considered by Kontsevich, Hinich and Manetti are equivalent, and are compatible with the derived stacks of Toen--Vezzosi and Lurie. Another application is that the cohomology groups associated to any classical deformation problem (in any characteristic) admit the same operations as Andre--Quillen cohomology.
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PDF链接：
https://arxiv.org/pdf/0705.0344
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