Theorems · Theorem · number theory
NumberField.InfinitePlace.mem_stabilizer_mk_iff
∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra k K] (φ : K →+* ℂ) (σ : Gal(K/k)),
σ ∈ MulAction.stabilizer Gal(K/k) (NumberField.InfinitePlace.mk φ) ↔ σ = 1 ∨ NumberField.ComplexEmbedding.IsConj φ σ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 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.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- Subgroupstatement · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- RingHom.compproof · cited by 899
- RingHomClass.toRingHomproof · cited by 746
- AlgEquiv.symmproof · cited by 615
- NumberField.InfinitePlacestatement · cited by 604
- MulAction.stabilizerstatement · cited by 254
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.exists_isConj_of_isRamifiedproof · cited by 1
- NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mkproof · cited by 1