Theorems · Theorem · algebraic geometry
Algebra.quasiFiniteAt_iff_isOpen_singleton_fiber
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.FiniteType R S] (q : PrimeSpectrum S), Algebra.QuasiFiniteAt R q.asIdeal ↔ IsOpen {⟨q, ⋯⟩}- Defined in
- Mathlib.RingTheory.ZariskisMainTheorem
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemstatement and proof · cited by 7,166
- Set.preimagestatement and proof · cited by 4,946
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsOpenstatement and proof · cited by 2,400
- Homeomorphproof · cited by 725
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealstatement and proof · cited by 333
- PrimeSpectrum.comapstatement and proof · cited by 199
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2