Theorems · Theorem · number theory
NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two
∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra k K]
{w : NumberField.InfinitePlace K} [IsGalois k K],
NumberField.InfinitePlace.IsRamified k w ↔ Nat.card ↥(MulAction.stabilizer Gal(K/k) w) = 2- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- AlgEquivstatement · cited by 1,681
- Nat.cardstatement · cited by 844
- NumberField.InfinitePlacestatement and proof · cited by 604
- MulAction.stabilizerstatement · cited by 254
- IsGaloisstatement and proof · cited by 149
- NumberField.InfinitePlace.IsRamifiedstatement · cited by 18
- NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_twoproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.exists_isConj_of_isRamifiedproof · cited by 1