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- W3037049585 abstract "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." @default.
- W3037049585 created "2020-07-02" @default.
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- W3037049585 date "2010-04-13" @default.
- W3037049585 modified "2023-09-27" @default.
- W3037049585 title "The defect" @default.
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