The regular inverse Galois problem over non-large fields | Zendy

Jochen Koenigsmann | Zendy

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The regular inverse Galois problem over non-large fields

Author(s) -

Jochen Koenigsmann

Publication year - 2004

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/15

Subject(s) - mathematics , embedding problem , galois group , differential galois theory , fundamental theorem of galois theory , galois extension , galois module , inverse , conjecture , galois theory , diophantine equation , function field , field (mathematics) , pure mathematics , galois cohomology , normal basis , discrete mathematics , geometry

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

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