Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 351-361 |
| Number of pages | 11 |
| Journal | Journal of the Institute of Mathematics of Jussieu |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2012 |
| Externally published | Yes |
Bibliographical note
Funding 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.
Keywords
- AMS 2010 Mathematics subject classificationPrimary 12E30;