Geodesic
Cyclic extensions and the local lifting problem
Andrew Obus1 ; Stefan Wewers2
1 Department of Mathematics, University of Virginia, Charlottesville VA 22904
2 Institut für Reine Mathematik, Universität Ulm, 89081 Ulm, Germany
Annals of mathematics, Tome 180 (2014) no. 1, pp. 233-284.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2014.180.1.5

Andrew Obus 1 ; Stefan Wewers 2

1 Department of Mathematics, University of Virginia, Charlottesville VA 22904
2 Institut für Reine Mathematik, Universität Ulm, 89081 Ulm, Germany 
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Andrew Obus; Stefan Wewers. Cyclic extensions and the local lifting problem. Annals of mathematics, Tome 180 (2014) no. 1, pp. 233-284. doi : 10.4007/annals.2014.180.1.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.180.1.5/

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