2023/07/07 by Jianing Yang, Yang, Jianing
Computer Science · Mathematics · #11G20 #13A35 #14B20 #14D10 #14H25 (secondary) #14H30 (primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2307.03819
openalex publication_date 2023/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a Galois cover of curves f over a field of characteristic p, the lifting problem asks whether there exists a Galois cover over a complete mixed characteristic discrete valuation ring whose reduction is f. In this paper, we consider the case where the Galois groups are elementary abelian p-groups. We prove a combinatorial criterion for lifting an elementary abelian p-cover, dependent on the branch loci of lifts of its p-cyclic subcovers. We also study how branch points of a lift coalesce on the special fiber. Finally, we analyze lifts for several families of (ℤ/2)3-covers of various conductor types, both with equidistant branch locus geometry and non-equidistant branch locus geometry.