Theorems · Definition · number theory
NumberField.CMExtension.equivMaximalRealSubfield
(F : Type u_1) →
(K : Type u_2) →
[inst : Field F] →
[NumberField.IsTotallyReal F] →
[inst_2 : Field K] →
[inst_3 : CharZero K] →
[Algebra.IsIntegral ℚ K] →
[NumberField.IsTotallyComplex K] →
[inst_6 : Algebra F K] → [Algebra.IsQuadraticExtension F K] → F ≃+* ↥(NumberField.maximalRealSubfield K)Any field F such that K/F is a CM-extension is isomorphic to the maximal real subfield of K.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Algebra.algebraMapproof · cited by 4,706
- RingEquivstatement · cited by 1,147
- CharZerostatement and proof · cited by 932
- Subfieldstatement · cited by 303
- Algebra.IsIntegralstatement and proof · cited by 224
- RingEquiv.transproof · cited by 54
- NumberField.maximalRealSubfieldstatement · cited by 38
- NumberField.IsTotallyRealstatement and proof · cited by 21
- NumberField.IsTotallyComplexstatement and proof · cited by 19
- Algebra.IsQuadraticExtensionstatement and proof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.CMExtension.equivMaximalRealSubfield_applystatement · cited by 1
- NumberField.CMExtension.equivMaximalRealSubfield.congr_simpstatement and proof · cited by 0
- NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_applystatement and proof · cited by 0