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24 June 2024
 
  » arxiv » 2302.00222

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A converse to the Hasse-Arf theorem
G. Griffith Elder ; Kevin Keating ;
Date 1 Feb 2023
AbstractLet $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$ be a nonabelian group which is isomorphic to the Galois group of some totally ramified extension $E/F$ of local fields with residue characteristic $p>2$. Then there is a totally ramified extension of local fields $L/K$ with residue characteristic $p$ such that Gal$(L/K)cong G$ and $L/K$ has at least one nonintegral upper ramification break.
Source arXiv, 2302.00222
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