The regular inverse Galois problem over non-large fields

Koenigsmann, Jochen. "The regular inverse Galois problem over non-large fields." Journal of the European Mathematical Society 006.4 (2004): 425-434. <http://eudml.org/doc/277220>.

@article{Koenigsmann2004,
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.},
author = {Koenigsmann, Jochen},
journal = {Journal of the European Mathematical Society},
keywords = {regular inverse Galois problem; embedding problems; large fields; Mordell conjecture for function fields; diophantine theory of fields; regular inverse Galois problem; embedding problems; large fields: Mordell conjecture for function fields; diophantine theory of fields},
language = {eng},
number = {4},
pages = {425-434},
publisher = {European Mathematical Society Publishing House},
title = {The regular inverse Galois problem over non-large fields},
url = {http://eudml.org/doc/277220},
volume = {006},
year = {2004},
}

TY - JOUR
AU - Koenigsmann, Jochen
TI - The regular inverse Galois problem over non-large fields
JO - Journal of the European Mathematical Society
PY - 2004
PB - European Mathematical Society Publishing House
VL - 006
IS - 4
SP - 425
EP - 434
AB - 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.
LA - eng
KW - regular inverse Galois problem; embedding problems; large fields; Mordell conjecture for function fields; diophantine theory of fields; regular inverse Galois problem; embedding problems; large fields: Mordell conjecture for function fields; diophantine theory of fields
UR - http://eudml.org/doc/277220
ER -