Theorems · Definition · number theory

NumberField.Units.basisOfIsMaxRank

{K : Type u_1} →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      {u : Fin (NumberField.Units.rank K) → (NumberField.RingOfIntegers K)ˣ} →
        NumberField.Units.IsMaxRank u →
          Module.Basis (Fin (NumberField.Units.rank K)) ℝ (NumberField.Units.dirichletUnitTheorem.logSpace K)

The images by logEmbedding of a family of units of maximal rank form a basis of logSpace K.

Defined in: Mathlib.NumberTheory.NumberField.Units.Regulator
Cited by: 9 results in Mathlib
Foundations: Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites15

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

Realstatement · cited by 25,697
Fieldstatement and proof · cited by 7,404
Equiv.symmproof · cited by 3,681
Unitsstatement and proof · cited by 2,804
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.RingOfIntegersstatement and proof · cited by 413
NumberField.Units.dirichletUnitTheorem.w₀statement · cited by 72
Module.Basis.reindexproof · cited by 57
NumberField.Units.rankstatement and proof · cited by 46
NumberField.Units.dirichletUnitTheorem.logSpacestatement · cited by 46

Cited by10

Results whose statement or proof uses this declaration.

NumberField.Units.regOfFamilyproof · cited by 12
NumberField.Units.regulator_eq_regOfFamily_fundSystemproof · cited by 7
NumberField.Units.regOfFamily_of_isMaxRankstatement and proof · cited by 4
NumberField.Units.regOfFamily_eq_det'proof · cited by 3
NumberField.Units.basisOfIsMaxRank_applystatement · cited by 3
NumberField.Units.regOfFamily_posproof · cited by 2
NumberField.Units.span_basisOfIsMaxRankstatement and proof · cited by 1
NumberField.Units.regOfFamily_div_regOfFamilyproof · cited by 1
NumberField.Units.basisOfIsMaxRank_fundSystemstatement and proof · cited by 1
NumberField.Units.basisOfIsMaxRank.congr_simpstatement and proof · cited by 0