Theorems · Theorem · algebraic geometry
PrimeSpectrum.exists_range_eq_of_isConstructible
∀ {R : Type u} [inst : CommRing R] {s : Set (PrimeSpectrum R)},
Topology.IsConstructible s → ∃ S x f, Set.range (PrimeSpectrum.comap f) = s[Stacks Tag 00F8](https://stacks.math.columbia.edu/tag/00F8) (without the finite presentation part)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
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
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Set.rangestatement and proof · cited by 4,705
- Compl.complproof · cited by 2,925
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClosed_of_stableUnderSpecialization_of_isConstructibleproof · cited by 1