Deforming cyclic covers in towers

2020/10/22 by Dang, Huy
#11S15 #14H10 #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.13614

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.

Related

• Lifting of Curves
• Fake Liftings of Galois Covers between Smooth Curves
• Cyclic p-groups and semi-stable reduction of curves in equal characteristic p>0
• The refined local lifting problem for cyclic covers of order four
• Cyclic Covers over Strongly Liftable Schemes