Line bundles and non-algebraically closed fields
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 \(X(K)\).
scientific article; zbMATH DE number 515183