Theorems · Definition · number theory

NumberField.equivReindex

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] → (K →+* ℂ) ≃ Module.Free.ChooseBasisIndex ℤ (NumberField.RingOfIntegers K)

An equivalence between the set of embeddings of K into ℂ and the index set of the chosen basis of the ring of integers of K.

Defined in: Mathlib.NumberTheory.NumberField.EquivReindex
Cited by: 7 results in Mathlib
Foundations: Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

RingHomstatement · cited by 10,189
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement · cited by 413
Module.Free.ChooseBasisIndexstatement · cited by 133
Fintype.equivOfCardEqproof · cited by 23

Cited by8

Results whose statement or proof uses this declaration.

NumberField.basisMatrixproof · cited by 9
NumberField.basisMatrix_eq_embeddingsMatrixReindexstatement and proof · cited by 2
NumberField.det_of_basisMatrix_non_zeroproof · cited by 1
NumberField.discr_eq_basisMatrix_det_sqproof · cited by 1
NumberField.inverse_basisMatrix_mulVec_eq_reprstatement and proof · cited by 1
NumberField.canonicalEmbedding_eq_basisMatrix_mulVecstatement and proof · cited by 1
NumberField.conj_basisMatrixproof · cited by 1
NumberField.house.basis_repr_norm_le_const_mul_housestatement · cited by 0