Theorems · Definition · number theory

NumberField.Units.basisUnitLattice

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] → Module.Basis (Fin (NumberField.Units.rank K)) ℤ ↥(NumberField.Units.unitLattice K)

The basis of the unitLattice obtained by mapping basisModTorsion via logEmbedding.

Defined in: Mathlib.NumberTheory.NumberField.Units.DirichletTheorem
Cited by: 16 results in Mathlib
Foundations: Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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

Cites13

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
Submodulestatement · cited by 7,192
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.Units.dirichletUnitTheorem.w₀statement · cited by 72
Module.Basis.mapproof · cited by 70
NumberField.Units.rankstatement · cited by 46
NumberField.Units.dirichletUnitTheorem.logSpacestatement · cited by 46
NumberField.Units.unitLatticestatement · cited by 21
NumberField.Units.logEmbeddingEquivproof · cited by 4

Cited by17

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalConeproof · cited by 22
NumberField.Units.regulator_eq_regOfFamily_fundSystemproof · cited by 7
NumberField.Units.isMaxRank_fundSystemproof · cited by 4
NumberField.Units.logEmbedding_fundSystemstatement · cited by 4
NumberField.mixedEmbedding.fundamentalCone.torsion_smul_mem_of_memproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamilyproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_memproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.unit_smul_mem_iff_mem_torsionproof · cited by 1
NumberField.mixedEmbedding.measurableSet_fundamentalConeproof · cited by 1
NumberField.Units.basisOfIsMaxRank_fundSystemstatement and proof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.exists_unit_smul_memproof · cited by 1
NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iffproof · cited by 1