Abstract
The Oort conjecture (now a theorem of Obus–Wewers and Pop) states that if k is an algebraically closed field of characteristic p , then any cyclic branched cover of smooth projective k -curves lifts to characteristic zero. This is equivalent to the local Oort conjecture, which states that all cyclic extensions of k[[t]] lift to characteristic zero. We generalize the local Oort conjecture to the case of Galois extensions with cyclic p -Sylow subgroups, reduce the conjecture to a pure characteristic p statement, and prove it in several cases. In particular, we show that D_9 is a so-called local Oort group .
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