Let R be a domain contained in a rank-1 valuation ring of its quotient field. Let R[X] be the ring of formal power series over R, and let F be the quotient field of R[X]. We prove that F is Hilbertian. This resolves and generalizes an open problem of Jarden, and allows to generalize previous Galois-theoretic results over fields of power series.
|Number of pages||11|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|State||Published - Apr 2012|
Bibliographical noteFunding Information:
Acknowledgements. The author was supported by an ERC grant while working on this research. The author thanks Arno Fehm, for many helpful suggestions and corrections, and the referee, for his/her comments.
- AMS 2010 Mathematics subject classificationPrimary 12E30;