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Theorems · Definition · number theory

NumberField.mixedEmbedding.fundamentalCone.equivFinRank

{K : Type u_1} →
  [inst : Field K] →
    [inst_1 : NumberField K] → Fin (NumberField.Units.rank K) ≃ { w // w ≠ NumberField.Units.dirichletUnitTheorem.w₀ }

A fixed equiv between Fin (rank K) and {w : InfinitePlace K // w ≠ w₀}.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by
10 results in Mathlib
Foundations
Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
Mathlib docsSourceLoogleLeanSearch

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NumberField.mixedEmbedding.fundamentalCone.completeFamily · cited by 5fundamentalCone.completeF…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'' · cited by 3fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne · cited by 3fundamentalCone.completeB…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply' · cited by 2fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily · cited by 2fundamentalCone.linearInd…NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamily · cited by 1fundamentalCone.sum_eq_ze…NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm · cited by 1fundamentalCone.abs_det_c…NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne · cited by 1fundamentalCone.expMap_ba…NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow · cited by 1fundamentalCone.prod_expM…NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne · cited by 1fundamentalCone.realSpace…NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis · cited by 0fundamentalCone.logMap_ex…Equiv · cited by 8337EquivField · cited by 7404FieldNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.Units.dirichletUnitTheorem.w₀ · cited by 72dirichletUnitTheorem.w₀NumberField.Units.rank · cited by 46Units.rankFintype.equivOfCardEq · cited by 23Fintype.equivOfCardEqfundamentalCone.equivFinRankCITED BYCITES

Cites7

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