# The regular inverse Galois problem over non-large fields

### Jochen Koenigsmann

University of Oxford, UK

## Abstract

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.

## Cite this article

Jochen Koenigsmann, The regular inverse Galois problem over non-large fields. J. Eur. Math. Soc. 6 (2004), no. 4, pp. 425–434

DOI 10.4171/JEMS/15