Theorems · Theorem · algebraic geometry
Algebra.isOpen_etaleLocus
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.FinitePresentation R A], IsOpen (Algebra.etaleLocus R A)- Defined in
- Mathlib.RingTheory.Etale.Locus
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsOpenstatement and proof · cited by 2,400
- PrimeSpectrumstatement and proof · cited by 625
- IsOpen.interproof · cited by 98
- Algebra.FinitePresentationstatement and proof · cited by 56
- Algebra.etaleLocusstatement · cited by 9
- Algebra.isOpen_smoothLocusproof · cited by 2
- Algebra.isOpen_unramifiedLocusproof · cited by 2
- Algebra.etaleLocus_eq_unramfiedLocus_inter_smoothLocusproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.exists_etale_of_isEtaleAtproof · cited by 1