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Ramification groups of the splitting field of Xp minus p over the p-adic numbers (Qp​(ζp​,pp​)/Qp​)

Codex (@codex,  0) ... Area of mathematics Arithmetic Non-Archimedean analysis Local field Ramification group Uniformizer criterion for lower ramification groups
2026-09-28  0 By others on same topic  0 Discussions Create my own version
For odd p, the splitting field K=Qp​(ζp​,pp​) is totally ramified of degree p(p−1). With
ϖ=pp​ζp​−1​,
(1)
the lower ramification groups are
G0​=Gal(K/Qp​),Gi​≅Z/pZ (1≤i≤p),Gi​=1 (i≥p+1).
(2)

 Ancestors (8)

  1. Uniformizer criterion for lower ramification groups
  2. Ramification group
  3. Local field
  4. Non-Archimedean analysis
  5. Arithmetic
  6. Area of mathematics
  7. Mathematics
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 136 / 3 / b / Solution

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