Line bundles and non-algebraically closed fields (Q1316341)
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scientific article; zbMATH DE number 515183
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Line bundles and non-algebraically closed fields |
scientific article; zbMATH DE number 515183 |
Statements
Line bundles and non-algebraically closed fields (English)
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5 March 1995
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Let \(k\) be a non-algebraically closed field, and let \(K\) be an algebraic closure of \(k\). Let \(X\) (resp. \(L)\) be an algebraic variety over \(k\) (resp. a line bundle on \(X)\). Then \(X(k)\) can be considered as a subset of \(X(K)\). The author relates the properties of \(k\) and the order of the restriction of \(L\) to an open neighbourhood of \(X(k)\) in \(X(K)\).
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closure of non-closed field
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algebraic variety
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line bundle
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