On ρ-extensions of ρ-adic fields
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...
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Durham University
2016
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| Online Access: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699527 |
| Summary: | 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. |
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