An obstruction to the local lifting problem

2023/04/17 by Aristides Kontogeorgis, Kontogeorgis, Aristides, Alexios Terezakis +1
Mathematics · #13D02 #14D15 #14H10 #14H37 #20C10 #20C20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2304.08377

openalex publication_date 2023/04/17 · openalex created_date 2023/04/20 · openalex updated_date 2026/07/28

Abstract

We are investigating the lifting problem for local actions involving semidirect products of a cyclic p-group with a cyclic group prime to p, where p represents the characteristic of the special fiber. We establish a criterion based on the Harbater-Katz-Gabber compactification of local actions, enabling us to determine whether a given local action can be lifted or not. Specifically, in the case of the dihedral group, we present an example of a local dihedral action that cannot be lifted. This instance provides a more potent obstruction than the KGB obstruction.

Related

• The local lifting problem for dihedral groups
• The local lifting problem for actions of finite groups on curves
• The Hurwitz tree obstruction for the refined local lifting problem
• The Local Lifting Problem for D₄
• Equidistant liftings of elementary abelian Galois covers of curves