Theorems · Theorem · commutative algebra
Ideal.comap_fiberIsoOfBijectiveResidueField_symm
∀ {R : Type u_1} {R' : Type u_2} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing R'] [inst_2 : CommRing S]
[inst_3 : Algebra R R'] [inst_4 : Algebra R S] {p : Ideal R} {q : Ideal R'} [inst_5 : p.IsPrime] [inst_6 : q.IsPrime]
[inst_7 : q.LiesOver p] (H : Function.Bijective ⇑(Ideal.ResidueField.mapₐ p q (Algebra.ofId R R') ⋯))
(Q : ↑(p.primesOver S)),
Ideal.comap ↑Algebra.TensorProduct.includeRight ↑((Ideal.fiberIsoOfBijectiveResidueField H).symm Q) = ↑Q- Defined in
- Mathlib.RingTheory.Etale.QuasiFinite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites58
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- RingHomstatement · cited by 10,189
- Set.Elemstatement and proof · cited by 7,166
- Set.preimageproof · cited by 4,946
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- one_mulproof · cited by 2,841
- TensorProductstatement and proof · cited by 2,545
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.comap_fiberIsoOfBijectiveResidueField_applyproof · cited by 1
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_auxproof · cited by 1