2021/07/05 by Dang, Huy
#11S15 #14H10 #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2107.01780
Suppose ϕ is a ℤ/4-cover of a curve over an algebraically closed field k of characteristic 2, and Φ1 is a nice lift of ϕ's ℤ/2-sub-cover to a complete discrete valuation ring R in characteristic zero. We show that there exist a finite extension R' of R, which is determined by Φ1, and a lift Φ of ϕ to R' whose ℤ/2-sub-cover isomorphic to Φ1 ⊗R R'. That result gives a non-trivial family of cyclic covers where Saïdi's refined lifting conjecture holds. In addition, the manuscript exhibits some phenomena that may shed some light on the mysterious moduli space of wildly ramified Galois covers.