Theorems · Definition · number theory

NumberField.FinitePlace.maximalIdeal

{K : Type u_1} →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      NumberField.FinitePlace K → IsDedekindDomain.HeightOneSpectrum (NumberField.RingOfIntegers K)

For a finite place w, return a maximal ideal v such that w = finite_place v .

Defined in: Mathlib.NumberTheory.NumberField.Completion.FinitePlace
Cited by: 10 results in Mathlib
Foundations: Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites5

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

Fieldstatement and proof · cited by 7,404
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement · cited by 413
IsDedekindDomain.HeightOneSpectrumstatement · cited by 338
NumberField.FinitePlacestatement and proof · cited by 35

Cited by11

Results whose statement or proof uses this declaration.

NumberField.FinitePlace.equivHeightOneSpectrumproof · cited by 7
NumberField.FinitePlace.hasFiniteMulSupport_intproof · cited by 3
NumberField.FinitePlace.mk_maximalIdealstatement · cited by 2
NumberField.FinitePlace.norm_embedding_eqstatement and proof · cited by 2
NumberField.FinitePlace.maximalIdeal_injectivestatement · cited by 2
NumberField.FinitePlace.equivHeightOneSpectrum_applystatement · cited by 1
NumberField.FinitePlace.apply_mul_absNorm_pow_eq_onestatement and proof · cited by 0
NumberField.FinitePlace.finprod_finitePlace_pow_multiplicitystatement and proof · cited by 0
NumberField.FinitePlace.hasFiniteMulSupport_fun_pow_multiplicitystatement and proof · cited by 0
NumberField.FinitePlace.maximalIdeal_injstatement · cited by 0
NumberField.FinitePlace.maximalIdeal_mkstatement · cited by 0