Theorems · Theorem · algebraic geometry
Algebra.IsEtaleAt.comp
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B]
[inst_3 : Algebra R A] [inst_4 : Algebra A B] [inst_5 : Algebra R B] [IsScalarTower R A B] (p : Ideal A) (P : Ideal B)
[P.LiesOver p] [inst_8 : p.IsPrime] [inst_9 : P.IsPrime] [Algebra.IsEtaleAt R p] [Algebra.IsEtaleAt A P],
Algebra.IsEtaleAt R P- Defined in
- Mathlib.RingTheory.Etale.Locus
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- IsScalarTowerstatement and proof · cited by 3,896
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplproof · cited by 462
- Localization.AtPrimeproof · cited by 299
- Ideal.LiesOverstatement and proof · cited by 272
- Algebra.FormallyEtaleproof · cited by 37
- Localization.AtPrime.algebraOfLiesOverproof · cited by 30
- Algebra.IsEtaleAtstatement and proof · cited by 5
- Algebra.FormallyEtale.compproof · cited by 5
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