Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd
∀ {m : ℕ} (p : 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})] [NeZero m]
[hK : IsCyclotomicExtension {m} ℚ K], ¬p ∣ m → P.inertiaDeg ℤ = orderOf ↑p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Equiv.symmproof · cited by 3,681
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Polynomial.natDegreeproof · cited by 1,105
- ZModstatement and proof · cited by 1,024
- Ideal.spanstatement and proof · cited by 948
- pow_oneproof · cited by 894
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvdproof · cited by 1