Abstract
Let k be an algebraically closed field of characteristic p>0. We study obstructions to lifting to characteristic 0 the faithful continuous action φ of a finite group G on k[[t]]. To each such φ a theorem of Katz and Gabber associates an action of G on a smooth projective curve Y over k. We say that the KGB obstruction of φ vanishes if G acts on a smooth projective curve X in characteristic 0 in such a way that X/H and Y/H have the same genus for all subgroups H⊂G. We determine for which G the KGB obstruction of every φ vanishes. We also consider analogous problems in which one requires only that an obstruction to lifting φ due to Bertin vanishes for some φ, or for all sufficiently ramified φ. These results provide evidence for the strengthening of Oort’s lifting conjecture which is discussed in [8, Conj. 1.2].
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