Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun_asIdeal

∀ {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 ⋯).toPresheafedSpace),
  (AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun f x).asIdeal =
    AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrier x

Defined in: Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme
Cited by: 0 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing SetLike AddSubgroupClass GradedRing

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CategoryTheory.Functor.objstatement · cited by 19,642
CommRingstatement and proof · cited by 17,173
Idealstatement · cited by 4,748
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
TopCatstatement · cited by 1,889
CommRingCat.carrierstatement · cited by 1,096
SetLikestatement and proof · cited by 1,084

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