Local-global principles for algebraic covers
The authors consider the following: Let \(B\) be an algebraic variety defined over a number field \(K\) and \(f:X\to B\) a cover a priori defined over \(\overline K\). Suppose \(f\) can be defined over each completion of \(K_v\) of \(K\). Does it follow that \(f\) can be defined over \(K\)? The authors prove that the answer is affirmative under some conditions.
scientific article; zbMATH DE number 1250647