Cyclic extensions and the local lifting problem


The local Oort conjecture states that, if $\Gamma$ is cyclic and $k$ is an algebraically closed field of characteristic $p$, then all $\Gamma$-extensions of $k[[t]]$ should lift to characteristic zero. We prove a critical case of this conjecture. In particular, we show that the conjecture is always true when $v_p(|\Gamma|) \leq 3$ and is true for arbitrarily highly $p$-divisible cyclic groups $\Gamma$ when a certain condition on the higher ramification filtration is satisfied.


Andrew Obus

Department of Mathematics, University of Virginia, Charlottesville VA 22904

Stefan Wewers

Institut für Reine Mathematik, Universität Ulm, 89081 Ulm, Germany