Hilbertianity of fields of power series

Publisher： Cambridge University Press

E-ISSN： 1475-3030|11|2|351-361

ISSN： 1474-7480

Source： Journal of the Institute of Mathematics of Jussieu, Vol.11, Iss.2, 2011-12, pp. : 351-361

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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.

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