Geodesic
The regular inverse Galois problem over non-large fields
Journal of the European Mathematical Society, Tome 6 (2004) no. 4, pp. 425-434.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/15
Classification : 12-XX, 00-XX
Keywords: Inverse Galois problem, embedding problems, large fields, Mordell conjecture for function fields, diophantine theory of fields 
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     author = {Jochen Koenigsmann},
     title = {The regular inverse {Galois} problem over non-large fields},
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Jochen Koenigsmann. The regular inverse Galois problem over non-large fields. Journal of the European Mathematical Society, Tome 6 (2004) no. 4, pp. 425-434. doi : 10.4171/jems/15. http://geodesic.mathdoc.fr/articles/10.4171/jems/15/

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