A non-PAC field whose maximal purely inseparable extension is PAC (Q1320033)
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scientific article; zbMATH DE number 554002
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A non-PAC field whose maximal purely inseparable extension is PAC |
scientific article; zbMATH DE number 554002 |
Statements
A non-PAC field whose maximal purely inseparable extension is PAC (English)
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22 November 1994
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If a field \(K\) is pseudo-algebraically closed (PAC), then each algebraic extension of \(K\) is PAC. \textit{W. D. Geyer} and \textit{M. Jarden} asked if the converse is true for purely inseparable extensions [Geom. Dedicata 29, 335-375 (1989; Zbl 0703.12006)]. Using the analogue of the Mordell conjecture for function fields, the author proves that there exists a non-PAC field whose maximal purely inseparable extension is PAC.
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pseudo-algebraically closed field
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purely inseparable extensions
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0.8257708549499512
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0.8135310411453247
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0.8065600395202637
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0.8037531971931458
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0.7888549566268921
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