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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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)
Uncontrolled Keywords Local fields; ramification filtration;
Divisions Faculty of Science > Mathematical Sciences, Department of
Date Deposited 24 Nov 2016 14:22
Last Modified 16 Mar 2026 17:54

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