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Automorphisms of Harbater-Katz-Gabber curves (1509.02139v2)
Published 7 Sep 2015 in math.AG and math.GR
Abstract: 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.