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    Title      l  Extension of Finite Solvable Torsors over a Curve
    Author   l  Marco Antei
    Date   l  2011-09-26
    Category   l  ASARC-Preprint-11-06
    Download    l 1317014156_0.812015.pdf  
Let $R$ be a complete discrete valuation ring with fraction field $K$ and with algebraically closed residue field of positive characteristic $p$. Let $X$ be a smooth fibered surface over $R$. Let $G$ be a finite, \'etale and solvable $K$-group scheme and assume that either $|G|=p^n$ or $G$ as a normal series of length $2$. e prove that for every connected and pointed $G$-torsor $Y$ over the generic fibre $X_{\eta}$ of $X$ there exist a regular fibered surface $\widetilde{X}$ over $R$ and a model map $\widetilde{X}\to X$ such that $Y$ can be extended to a torsor over $\widetilde{X}$ possibly after xtending scalars.