Theorems · Theorem · algebraic geometry

AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocally

∀ {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.PropertyIsLocal fun {R S} [CommRing R] [CommRing S] => Q) →
    ∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y),
      AlgebraicGeometry.targetAffineLocally (AlgebraicGeometry.affineAnd fun {R S} [CommRing R] [CommRing S] => Q) f ↔
        AlgebraicGeometry.IsAffineHom f ∧ AlgebraicGeometry.affineLocally (fun {R S} [CommRing R] [CommRing S] => Q) f

Defined in: Mathlib.AlgebraicGeometry.Morphisms.AffineAnd
Cited by: 1 results in Mathlib
Foundations: Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

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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.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
Quiver.Hom.opproof · cited by 1,948
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocallyproof · cited by 1