Theorems · Definition · number theory
NumberField.IsCMField.equivInfinitePlace
(K : Type u_1) →
[inst : Field K] →
[inst_1 : CharZero K] →
[NumberField.IsCMField K] →
[NumberField K] → NumberField.InfinitePlace K ≃ NumberField.InfinitePlace ↥(NumberField.maximalRealSubfield K)The equiv between the infinite places of K and the infinite places of K⁺ induced by the
restriction to K⁺, see equivInfinitePlace_apply.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 302 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.
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- CharZerostatement and proof · cited by 932
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement and proof · cited by 604
- Subfieldstatement · cited by 303
- Equiv.ofBijectiveproof · cited by 70
- NumberField.InfinitePlace.comapproof · cited by 55
- NumberField.IsCMFieldstatement and proof · cited by 45
- NumberField.maximalRealSubfieldstatement and proof · cited by 38
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.equivInfinitePlace_applystatement · cited by 1
- NumberField.IsCMField.equivInfinitePlace_symm_applystatement and proof · cited by 1
- NumberField.IsCMField.regOfFamily_realFunSystemproof · cited by 1
- NumberField.IsCMField.equivInfinitePlace.congr_simpstatement and proof · cited by 0