We show that there is a field complete with respect to a discrete valuation whose residue field is perfect and there is a finite Galois extension such that there is no solvable Galois extension such that the extension is unramified, where is the composite of and . As an application we deduce that that there is a field as above and there is a smooth, projective, geometrically irreducible curve over which does not acquire semi-stable reduction over any solvable extension of .
Cite this article
Ambrus Pál, Curves which do not Become Semi-Stable After any Solvable Extension. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 265–276DOI 10.4171/RSMUP/129-15