Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.prime

∀ {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} {m : ℕ} (f_deg : f ∈ 𝒜 m) (hm : 0 < m)
  (q :
    ↑↑(AlgebraicGeometry.Spec.locallyRingedSpaceObj
            (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))).toPresheafedSpace),
  (AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal f_deg hm q).IsPrime

Defined in: Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme
Cited by: 0 results in Mathlib
Foundations: Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing SetLike AddSubgroupClass GradedRing

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Cites55

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Idealproof · cited by 4,748
TopCat.carrierstatement and proof · cited by 3,184
Submonoidproof · cited by 3,086
CommRingCatstatement · cited by 2,333
CommMonoidproof · cited by 2,264
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
LT.lt.ne'proof · cited by 1,417
CommRingCat.carrierproof · cited by 1,096

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFunproof · cited by 4