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Apr 26, 2020 at 22:14 vote accept yshuai Qin
Apr 26, 2020 at 16:02 answer added Johan timeline score: 3
Apr 22, 2020 at 14:15 comment added Jef Very roughly, the field $K(Y)$ only depends on the generic fiber of $Y$, and the extension $K(Y)/K(X)$ will be Galois if and only if $\text{Frac}(R_1)//\text{Frac}(R)$ is Galois. Now it suffices to note that there exists a semistable model over any finite extension of $R_1$, for which we can take the Galois closure of the fraction field of $R_1$.
Apr 22, 2020 at 11:17 history asked yshuai Qin CC BY-SA 4.0