Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Automorphisms of local fields of period $p^M$ and nilpotent class $<p$ (1505.05352v2)

Published 20 May 2015 in math.NT

Abstract: Suppose $K$ is a finite extension of $\mathbb{Q}_p$ containing a $pM$-th primitive root of unity. For $1\leqslant s<p$ denote by $K[s,M]$ the maximal $p$-extension of $K$ with the Galois group of period $p^M$ and nilpotent class $s$. We apply the nilpotent Artin-Schreier theory together with the theory of the field-of-norms functor to give an explicit description of the Galois groups ${Gal}(K[s,M]/K)$. As application we prove that the ramification subgroup $\Gamma ^{(v)}_K$ of the absolute Galois group of $K$ acts trivially on $K[s,M]$ if and only if $v>e_K(M+s/(p-1))-(1-\delta _{1s})/p$, where $e_K$ is the ramification index of $K$ and $\delta _{1s}$ is the Kronecker symbol.

Summary

We haven't generated a summary for this paper yet.