Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.ramificationIdx_eq_of_prime_pow
∀ (p k : ℕ) [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
[hK : IsCyclotomicExtension {p ^ (k + 1)} ℚ K] (P : Ideal (NumberField.RingOfIntegers K)) [hP₁ : P.IsPrime]
[hP₂ : P.LiesOver (Ideal.span {↑p})], P.ramificationIdx ℤ = p ^ k * (p - 1)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsPrimestatement and proof · cited by 827
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Ideal.LiesOverstatement and proof · cited by 272
- IsCyclotomicExtensionstatement and proof · cited by 220
- Ideal.ramificationIdxstatement and proof · cited by 59
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