A converse to the Hasse-Arf theorem

2023/02/01 by Elder, G. Griffith, Keating, Kevin
#11S15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.00222

Abstract

Let 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)≅ G and L/K has at least one nonintegral upper ramification break.

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