Theorems · Theorem · algebraic geometry

PrimeSpectrum.preimageEquivFiber_symm_apply_coe

∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : PrimeSpectrum R)
  (q : PrimeSpectrum (p.asIdeal.Fiber S)),
  ↑((PrimeSpectrum.preimageEquivFiber R S p).symm q) =
    PrimeSpectrum.comap Algebra.TensorProduct.includeRight.toRingHom q

Defined in: Mathlib.RingTheory.LocalRing.ResidueField.Fiber
Cited by: 0 results in Mathlib
Foundations: Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra

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DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Equivstatement · cited by 8,337
Set.Elemstatement · cited by 7,166
Set.preimagestatement · cited by 4,946
Algebra.algebraMapstatement · cited by 4,706
Equiv.symmstatement and proof · cited by 3,681
TensorProductstatement · cited by 2,545
PrimeSpectrumstatement and proof · cited by 625
AlgHom.toRingHomstatement · cited by 490

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