English

Deforming cyclic covers in towers

Algebraic Geometry 2023-12-21 v4 Number Theory

Abstract

Obus-Wewers and Pop recently resolved a long-standing conjecture by Oort that says: every cyclic cover of a curve in characteristic p>0p>0 lifts to characteristic zero. Sa\"idi 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.

Cite

@article{arxiv.2010.13614,
  title  = {Deforming cyclic covers in towers},
  author = {Huy Dang},
  journal= {arXiv preprint arXiv:2010.13614},
  year   = {2023}
}

Comments

Proofread 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

R2 v1 2026-06-23T19:39:19.122Z