Theorems · Definition · algebraic geometry
AlgebraicGeometry.PrimeSpectrum.Top
(R : Type u) → [CommRing R] → TopCat
The prime spectrum as an object of TopCat.
- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 77 from the axioms, rests on 984 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- TopCatstatement · cited by 1,889
- PrimeSpectrumproof · cited by 625
Cited by136
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.structureSheafInTypestatement · cited by 59
- AlgebraicGeometry.Spec.structureSheafstatement · cited by 57
- AlgebraicGeometry.structurePresheafInCommRingCatstatement and proof · cited by 23
- AlgebraicGeometry.StructureSheaf.toStalkstatement and proof · cited by 21
- AlgebraicGeometry.StructureSheaf.conststatement and proof · cited by 20
- AlgebraicGeometry.StructureSheaf.Localizationsstatement and proof · cited by 15
- AlgebraicGeometry.StructureSheaf.comapstatement and proof · cited by 15
- AlgebraicGeometry.StructureSheaf.isLocallyFractionstatement · cited by 8
- AlgebraicGeometry.StructureSheaf.algebraMap_germstatement and proof · cited by 6
- AlgebraicGeometry.StructureSheaf.comap_applystatement and proof · cited by 5
- AlgebraicGeometry.StructureSheaf.stalkIsostatement · cited by 5
- AlgebraicGeometry.tilde.toOpen_resstatement and proof · cited by 4