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Title: On ρ-extensions of ρ-adic fields
Author: McCabe, Keith Thomas
ISNI:       0000 0004 5990 0388
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2016
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Let ρ be an odd prime, and let K be a finite extension of Qp such that K contains a primitive ρ-th root of unity. Let K <ρ be the maximal ρ-extension of K with Galois group Γ <ρ of period ρ and nilpotence class < ρ. Recent results of Abrashkin describe the ramification filtration ?, and can be used to recover the structure of Γ< ρ. The group Γ< ρ is described in terms of an Fρ- Lie algebra L due to the classical equivalence of categories of Fρ-Lie algebras of nilpotent class < ρ, and ρ-groups of period ρ of the same nilpotent class. In this thesis we generalise explicit calculations of Abrashkin related to the structure of Γ< ρ.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available