Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.map_preimage_basicOpen

∀ {A B σ τ : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] [inst_3 : CommRing B]
  [inst_4 : SetLike τ B] [inst_5 : AddSubgroupClass τ B] {𝒜 : ℕ → σ} {ℬ : ℕ → τ} [inst_6 : GradedRing 𝒜]
  [inst_7 : GradedRing ℬ] (f : 𝒜 →+*ᵍ ℬ)
  (hf : HomogeneousIdeal.irrelevant ℬ ≤ HomogeneousIdeal.map f (HomogeneousIdeal.irrelevant 𝒜)) (s : A),
  (TopologicalSpace.Opens.map (AlgebraicGeometry.Proj.map f hf).base).obj (AlgebraicGeometry.Proj.basicOpen 𝒜 s) =
    AlgebraicGeometry.Proj.basicOpen ℬ (f s)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Functor

Cited by

0 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassCommRingSetLikeAddSubgroupClassGradedRingGradedRing