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A converse to the HasseArf theorem  G. Griffith Elder
; Kevin Keating
;  Date: 
1 Feb 2023  Abstract:  Let $L/K$ be a finite Galois extension of local fields. The HasseArf 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 HasseArf 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  Services:  Forum  Review  PDF  Favorites 


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