Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.inertiaDeg_eq
∀ (n : ℕ) {m p k : ℕ} [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
(P : Ideal (NumberField.RingOfIntegers K)) [hP₁ : P.IsPrime] [hP₂ : P.LiesOver (Ideal.span {↑p})]
[IsCyclotomicExtension {n} ℚ K], n = p ^ (k + 1) * m → ¬p ∣ m → P.inertiaDeg ℤ = orderOf ↑p- Cited by
- 0 results in Mathlib
- Foundations
- Depth 326 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
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
- AlgEquivproof · cited by 1,681
- ZModstatement · cited by 1,024
- 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
- orderOfstatement and proof · cited by 324
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