Theorems · Theorem · algebraic geometry
Algebra.isOpen_unramifiedLocus
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.EssFiniteType R A], IsOpen (Algebra.unramifiedLocus R A)- Defined in
- Mathlib.RingTheory.Unramified.Locus
- Cited by
- 2 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.
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
- Compl.complproof · cited by 2,925
- IsOpenstatement and proof · cited by 2,400
- PrimeSpectrumstatement and proof · cited by 625
- IsClosed.isOpen_complproof · cited by 126
- Algebra.EssFiniteTypestatement and proof · cited by 68
- Module.support_eq_zeroLocusproof · cited by 10
- Algebra.unramifiedLocusstatement · cited by 6
- Algebra.unramifiedLocus_eq_compl_supportproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.exists_formallyUnramified_of_isUnramifiedAtproof · cited by 2
- Algebra.isOpen_etaleLocusproof · cited by 1