缺陷
The defect
摘要：
介绍了估值理论中的“缺陷”现象，也称“衍生缺陷”。我们描述了它在正特征性的深开问题中所起的作用：局部单值化（奇点的奇点的分解的局部形式），值域的模型论，值函数域的结构论。我们给出了几个具有非平凡亏损的代数扩张的例子。我们指出为什么Artin-Schreier缺陷扩展起着核心作用，并描述了一种方法来分类它们。此外，我们给出了一个概述的各种结果的缺陷，有助于驯服或避免它，特别是“稳定性”定理和定理的“亨氏理性”，并显示它们是如何应用。最后，我们列出了一个开放的问题。
英文摘要：
We give an introduction to the valuation theoretical phenomenon of "defect", also known as "ramification deficiency". We describe the role it plays in deep open problems in positive characteristic: local uniformization (the local form of resolution of singularities), the model theory of valued fields, the structure theory of valued function fields. We give several examples of algebraic extensions with non-trivial defect. We indicate why Artin-Schreier defect extensions play a central role and describe a way to classify them. Further, we give an overview of various results about the defect that help to tame or avoid it, in particular "stability" theorems and theorems on "henselian rationality", and show how they are applied. Finally, we include a list of open problems.
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