Theorems · Theorem · commutative algebra
Algebra.IsSmoothAt.of_formallySmooth_fiber
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.Flat R S]
[Algebra.FinitePresentation R S] (p : Ideal R) (q : Ideal S) [inst_5 : p.IsPrime] [inst_6 : q.IsPrime] [q.LiesOver p]
[Algebra.FormallySmooth p.ResidueField (p.Fiber S)], Algebra.IsSmoothAt R q[Stacks Tag 00TF](https://stacks.math.columbia.edu/tag/00TF) (We require the whole fiber to be smooth instead)
- Defined in
- Mathlib.RingTheory.Smooth.Fiber
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites64
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
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- AlgHomproof · cited by 3,236
- TensorProductproof · cited by 2,545
- AlgEquivproof · cited by 1,681
- IsUnitproof · cited by 1,602
- RingHom.compproof · cited by 899
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Smooth.of_formallySmooth_fiberproof · cited by 2