The regular inverse Galois problem over non-large fields
Summary: By a celebrated theorem of Harbater and Pop, the regular inverse Galois problem is solvable over any field containing a large field. Using this and the Mordell conjecture for function fields, we construct the first example of a field \(K\) over which the regular inverse Galois problem can be shown to be solvable, but such that \(K\) does not contain a large field. The paper is complemented by model-theoretic observations on the diophantine nature of the regular inverse Galois problem.
large fields: Mordell conjecture for function fields
scientific article; zbMATH DE number 2139678