# The regular inverse Galois problem over non-large fields

Journal of the European Mathematical Society (2004)

- Volume: 006, Issue: 4, page 425-434
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topKoenigsmann, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.