Deforming cyclic covers in towers

Abstract

Obus-Wewers and Pop recently resolved a long-standing conjecture by Oort that says: every cyclic cover of a curve in characteristic $p>0$ lifts to characteristic zero. Saïdi further asks whether these covers are also "liftable in towers". We prove that the answer for the equal-characteristic version of this question is affirmative. Our proof employs the Hurwitz tree technique and the tools developed by Obus-Wewers.

arXiv commentProofread and corrected errors in the proof of Proposition 4.20. Added Proposition 4.14. The updated document includes 66 pages, 4 figures, and 6 tables