Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvd
∀ {m : ℕ} (p : ℕ) [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] [NeZero m]
[hK : IsCyclotomicExtension {m} ℚ K],
¬p ∣ m → (Ideal.span {↑p}).inertiaDegIn (NumberField.RingOfIntegers K) = orderOf ↑p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 323 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Set.Elemproof · cited by 7,166
- Idealproof · 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.IsPrimeproof · cited by 827
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.galEquivZMod_stabilizerproof · cited by 0