Theorems · Theorem · number theory
NumberField.InfinitePlace.card_stabilizer
∀ {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],
Nat.card ↥(MulAction.stabilizer Gal(K/k) w) = if NumberField.InfinitePlace.IsUnramified k w then 1 else 2- Cited by
- 2 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.
Cites11
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 and proof · cited by 1,681
- Nat.cardstatement and proof · cited by 844
- NumberField.InfinitePlacestatement and proof · cited by 604
- MulAction.stabilizerstatement and proof · cited by 254
- IsGaloisstatement and proof · cited by 149
- NumberField.InfinitePlace.IsUnramifiedstatement and proof · cited by 35
- NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_twoproof · cited by 3
- NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_oneproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.card_isUnramifiedproof · cited by 1
- NumberField.InfinitePlace.card_isUnramified_complproof · cited by 1