Abstract
Consider a valuation ringR of a discrete Henselian field and a positive integerr. LetF be the quotient field of the ringR[[X1, …,Xr]]. We prove that every finite group occurs as a Galois group overF. In particular, ifK0 is an arbitrary field andr≥2, then every finite group occurs as a Galois group overK0((X1, …,Xr)).
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