Automorphisms of Harbater-Katz-Gabber curves
arXiv:1509.02139 · doi:10.1007/s00208-016-1490-2
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.
25 pages. The introduction was rewritten. The final publication is available at Springer via http://dx.doi.org/10.1007/s00208-016-1490-2