Theorems · Theorem · algebraic geometry
MaximalSpectrum.toPiLocalizationEquiv_apply_apply
∀ (R : Type u) [inst : CommSemiring R] [inst_1 : DiscreteTopology (PrimeSpectrum R)] (x : R) (I : MaximalSpectrum R), (MaximalSpectrum.toPiLocalizationEquiv R) x I = (algebraMap R (Localization.AtPrime I.asIdeal)) x
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDiscreteTopology
Around this declaration
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.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- AlgEquivstatement · cited by 1,681
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplstatement · cited by 462
- DiscreteTopologystatement and proof · cited by 373
- Localization.AtPrimestatement · cited by 299
- MaximalSpectrumstatement and proof · cited by 73
- MaximalSpectrum.asIdealstatement · cited by 58
- MaximalSpectrum.PiLocalizationstatement · cited by 17
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.