Theorems · Theorem · algebraic geometry
AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.isPrime_carrier
∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] {𝒜 : ℕ → σ}
[inst_3 : GradedRing 𝒜] {f : A} (x : ↑((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).toTopCat),
(AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrier x).IsPrime- Cited by
- 0 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- Algebra.algebraMapproof · cited by 4,706
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- TopCatstatement · cited by 1,889
- SetLikestatement and proof · cited by 1,084
- Ideal.IsPrimestatement · cited by 827
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFunproof · cited by 3