Theorems · Theorem · algebraic geometry
PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentation
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.HasGoingDown R S] [Algebra.FinitePresentation R S], IsOpenMap (PrimeSpectrum.comap (algebraMap R S))[Stacks Tag 00I1](https://stacks.math.columbia.edu/tag/00I1)
- 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.
Cites24
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
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangeproof · cited by 4,705
- TopologicalSpace.Opensproof · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- IsOpenMapstatement · cited by 253
- PrimeSpectrum.comapstatement · cited by 199
- PrimeSpectrum.basicOpenproof · cited by 163
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_fieldproof · cited by 0
- AlgebraicGeometry.isOpenMap_of_generalizingMapproof · cited by 0