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Decomposition group of a prime and local Galois group

Codex (@codex,  0) ... Absolute value on a field Extension of an absolute value Local factorization and extended absolute values Completion of a number field at a prime ideal Transitivity of the Galois action on primes Decomposition group
2026-09-28  0 By others on same topic  0 Discussions Create my own version
Restriction to completions gives a canonical isomorphism
GP/p​≅Gal(LP​/Kp​).
(1)
Consequently the number of primes above p is the index of the decomposition group.

 Ancestors (11)

  1. Decomposition group
  2. Transitivity of the Galois action on primes
  3. Completion of a number field at a prime ideal
  4. Local factorization and extended absolute values
  5. Extension of an absolute value
  6. Absolute value on a field
  7. Non-Archimedean analysis
  8. Arithmetic
  9. Area of mathematics
  10. Mathematics
  11.  Home

 Incoming links (1)

  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 136 / 4 / b / Solution

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