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

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



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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