Theorems · Theorem · algebraic geometry
Algebra.IsEtaleAt.exists_isStandardEtale
∀ {R : Type u_1} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (Q : Ideal S)
[inst_3 : Q.IsPrime] [Algebra.FinitePresentation R S] [Algebra.IsEtaleAt R Q],
∃ f ∉ Q, Algebra.IsStandardEtale R (Localization.Away f)[Stacks Tag 00UE](https://stacks.math.columbia.edu/tag/00UE)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Ideal.IsPrimestatement and proof · cited by 827
- Submonoid.powersstatement · cited by 408
- Localization.Awaystatement and proof · cited by 162
- Algebra.FinitePresentationstatement and proof · cited by 56
- Algebra.Etaleproof · cited by 34
- Algebra.IsStandardEtalestatement · cited by 10
- Ideal.IsPrime.mul_notMemproof · cited by 8
- HasStandardEtaleSurjectionOnproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomialproof · cited by 1