JournalscmhVol. 92, No. 3pp. 551–620

A generalization of the Oort conjecture

  • Andrew Obus

    University of Virginia, Charlottesville, USA
A generalization of the Oort conjecture cover

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Abstract

The Oort conjecture (now a theorem of Obus–Wewers and Pop) states that if kk is an algebraically closed field of characteristic pp, then any cyclic branched cover of smooth projective kk-curves lifts to characteristic zero. This is equivalent to the local Oort conjecture, which states that all cyclic extensions of k[[t]]k[[t]] lift to characteristic zero. We generalize the local Oort conjecture to the case of Galois extensions with cyclic pp-Sylow subgroups, reduce the conjecture to a pure characteristic pp statement, and prove it in several cases. In particular, we show that D9D_9 is a so-called local Oort group.

Cite this article

Andrew Obus, A generalization of the Oort conjecture. Comment. Math. Helv. 92 (2017), no. 3, pp. 551–620

DOI 10.4171/CMH/419