Theorems · Theorem · algebraic geometry
Algebra.IsUnramifiedAt.residueField
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (P : Ideal R)
[inst_3 : P.IsPrime] (Q : Ideal A) [inst_4 : Q.IsPrime] [Q.LiesOver P] [Algebra.IsUnramifiedAt R Q]
(Q' : Ideal (P.Fiber A)) [inst_7 : Q'.IsPrime],
Q = Ideal.comap Algebra.TensorProduct.includeRight.toRingHom Q' → Algebra.IsUnramifiedAt P.ResidueField Q'If A is an R-algebra unramified at Q, P is the prime of R lying under Q,
then κ(P) ⊗ A is unramified at Q' (the prime corresponding to Q) over κ(P).
- Defined in
- Mathlib.RingTheory.Unramified.Locus
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- one_mulproof · cited by 2,841
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- map_oneproof · cited by 861
- Ideal.IsPrimestatement and proof · cited by 827
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.