ملخص
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.
اللغة الأصلية | الإنجليزيّة |
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الصفحات (من إلى) | 351-361 |
عدد الصفحات | 11 |
دورية | Journal of the Institute of Mathematics of Jussieu |
مستوى الصوت | 11 |
رقم الإصدار | 2 |
المعرِّفات الرقمية للأشياء | |
حالة النشر | نُشِر - أبريل 2012 |
منشور خارجيًا | نعم |
ملاحظة ببليوغرافية
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.