Automorphisms of Harbater-Katz-Gabber curves
© 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 th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer Nature,
2021-10-27T20:05:25Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | © 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. |
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