A generalization of the Oort conjecture

  • Andrew Obus

    University of Virginia, Charlottesville, USA

Abstract

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