Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.ideal_map

∀ {X Y : AlgebraicGeometry.Scheme} (I : X.IdealSheafData) (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f]
  (U : ↑Y.affineOpens) (H : AlgebraicGeometry.IsAffineOpen ((TopologicalSpace.Opens.map f.base).obj ↑U)),
  (I.map f).ideal U =
    Ideal.comap (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.app f ↑U))
      (I.ideal ⟨(TopologicalSpace.Opens.map f.base).obj ↑U, H⟩)

Defined in: Mathlib.AlgebraicGeometry.IdealSheaf.Functorial
Cited by: 1 results in Mathlib
Foundations: Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.QuasiCompact

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

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AlgebraicGeometry.Schemestatement and proof · cited by 2,540

Cited by1

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AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHomproof · cited by 0