The regular inverse Galois problem over non-large fields

Author: 

Koenigsmann, J

Publication Date: 

1 January 2004

Journal: 

Journal of the European Mathematical Society

Last Updated: 

2019-04-26T16:21:05.657+01:00

Issue: 

4

Volume: 

6

DOI: 

10.4171/JEMS/15

page: 

425-434

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.

Symplectic id: 

28108

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article