JournalsrsmupVol. 129pp. 265–276

Curves which do not Become Semi-Stable After any Solvable Extension

  • Ambrus Pál

    Imperial College, London, UK
Curves which do not Become Semi-Stable After any Solvable Extension cover
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Abstract

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

Cite this article

Ambrus Pál, Curves which do not Become Semi-Stable After any Solvable Extension. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 265–276

DOI 10.4171/RSMUP/129-15