Geodesic
The regular inverse Galois problem over non-large fields
Journal of the European Mathematical Society, Tome 6 (2004) no. 4, pp. 425-434 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2004_6_4_a1,
     author = {Jochen Koenigsmann},
     title = {The regular inverse {Galois} problem over non-large fields},
     journal = {Journal of the European Mathematical Society},
     pages = {425--434},
     year = {2004},
     volume = {6},
     number = {4},
     doi = {10.4171/jems/15},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/15/}
}
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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

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