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The regular inverse Galois problem over non-large fields

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.
Publication status:
Published

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Publisher copy:
10.4171/JEMS/15

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume:
6
Issue:
4
Pages:
425-434
Publication date:
2004-10-05
DOI:
ISSN:
1435-9855
URN:
uuid:8ea5f39d-9fba-45c9-af2e-4d734c3aca5d
Source identifiers:
28108
Local pid:
pubs:28108

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