Theorems · Theorem · algebraic geometry
PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal
∀ (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.comap (algebraMap R S) ⁻¹' {p})),
↑((PrimeSpectrum.preimageOrderIsoFiber R S p) q).asIdeal =
⇑(Algebra.TensorProduct.lift (Ideal.ResidueField.mapₐ p.asIdeal (↑q).asIdeal (Algebra.ofId R S) ⋯)
(IsScalarTower.toAlgHom R S (↑q).asIdeal.ResidueField) ⋯) ⁻¹'
{0}- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
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- Submodulestatement · cited by 7,192
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- Set.preimagestatement and proof · cited by 4,946
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement · cited by 3,236
- TensorProductstatement · cited by 2,545
- PrimeSpectrumstatement and proof · cited by 625
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