On $p$ -extensions of $p$ -adic fields

MCCABE, KEITH,THOMAS (2016) On $p$ -extensions of $p$ -adic fields. Doctoral thesis, Durham University.

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Abstract

Let $p$ be an odd prime, and let $K$ be a $p$ -adic field containing a primitive $p$ -th root of unity. Let $K_{<p}$ be the maximal $p$ -extension of $K$ with Galois group $\Gamma_{<p}$ of period $p$ and nilpotence class $<p$ . Recent results of Abrashkin describe the ramification filtration $\big{\{} \Gamma_{<p}^{(v)} \big{\}}$ , and can be used to recover the structure of $\Gamma_{<p}$ .

The group $\Gamma_{<p}$ is described in terms of an $\mathbb{F}_p$ -Lie algebra $L$ due to the classical equivalence of categories of $\mathbb{F}_p$ -Lie algebras of nilpotent class $<p$ , and $p$ -groups of period $p$ of the same nilpotent class. In this thesis we generalise explicit calculations of Abrashkin related to the structure of $\Gamma_{<p}$ .

Item Type:	Thesis (Doctoral)
Award:	Doctor of Philosophy
Keywords:	Local fields; ramification filtration;
Faculty and Department:	Faculty of Science > Mathematical Sciences, Department of
Thesis Date:	2016
Copyright:	Copyright of this thesis is held by the author
Deposited On:	24 Nov 2016 14:22

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