Abstract
We show that there is a field F complete with respect to a discrete valuation whose residue field is perfect and there is a finite Galois extension K\vert F such that there is no solvable Galois extension L\vert F such that the extension KL\vert K is unramified, where KL is the composite of K and L . As an application we deduce that that there is a field F as above and there is a smooth, projective, geometrically irreducible curve over F which does not acquire semi-stable reduction over any solvable extension of F .
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