Rendiconti del Seminario Matematico della Università di Padova


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Volume 129, 2013, pp. 265–276
DOI: 10.4171/RSMUP/129-15

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

Ambrus Pál[1]

(1) Imperial College, London, UK

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 $F$.

Keywords: Local fields, abelian varieties, semistable reduction

Pál Ambrus: Curves which do not Become Semi-Stable After any Solvable Extension. Rend. Sem. Mat. Univ. Padova 129 (2013), 265-276. doi: 10.4171/RSMUP/129-15