The Oort Conjecture on  lifting covers of curves

Florian Pop

doi:https://doi.org/10.4007/annals.2014.180.1.6

The Oort Conjecture on lifting covers of curves

Pages 285-322 from Volume 180 (2014), Issue 1 by Florian Pop

Abstract

We show that the conjecture of Oort on lifting covers of curves is true. The main ingredients in the proof are a deformation argument in characteristic $p$ and (a special case of) a very recent result by Obus–Wewers. A kind of boundedness result is given as well.

Keywords

Artin--Schreier--Witt theory, Galois $G$-covers of curves, Hilbert ramification theory, Oort conjecture, Witt vectors, lifting of $G$-covers, smooth curves over valuation rings

DOI

https://doi.org/10.4007/annals.2014.180.1.6

3194816

zbMATH

06316071

Milestones

Received: 17 May 2012
Revised: 7 August 2013
Accepted: 25 September 2013
Published online: 1 July 2014