Automorphisms of Harbater–Katz–Gabber curves

Abstract

© 2016, Springer-Verlag Berlin Heidelberg. Let k be a perfect field of characteristic p> 0 , and let G be a finite group. We consider the pointed G-curves over k associated by Harbater, Katz, and Gabber to faithful actions of G on k[[t]] over k. We use such “HKG G-curves” to classify the automorphisms of k[[t]] of p-power order that can be expressed by particularly explicit formulas, namely those mapping t to a power series lying in a Z/ pZ Artin–Schreier extension of k(t). In addition, we give necessary and sufficient criteria to decide when an HKG G-curve with an action of a larger finite group J is also an HKG J-curve.