JournalsjemsVol. 6, No. 4pp. 425–434

The regular inverse Galois problem over non-large fields

  • Jochen Koenigsmann

    University of Oxford, UK
The regular inverse Galois problem over non-large fields cover
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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 KK over which the regular inverse Galois problem can be shown to be solvable, but such that KK 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