Theorems · Theorem · algebraic geometry
PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : p.IsPrime] (q : PrimeSpectrum (p.Fiber S)),
↑((PrimeSpectrum.primesOverOrderIsoFiber R S p).symm q) = Ideal.comap Algebra.TensorProduct.includeRight q.asIdeal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemstatement · cited by 7,166
- Idealstatement and proof · cited by 4,748
- AlgHomstatement · cited by 3,236
- TensorProductstatement · cited by 2,545
- OrderIsostatement · cited by 874
- Ideal.IsPrimestatement and proof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- OrderIso.symmstatement · cited by 475
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_posproof · cited by 5