Abstract
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, étale and solvable K-group scheme and assume that either |G| = p n or G has a normal series of length 2. We 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 extending scalars.
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