Theorems · Theorem · algebraic geometry

AlgebraicGeometry.affineLocally_iff_affineOpens_le

∀ (P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) {X Y : AlgebraicGeometry.Scheme}
  (f : X ⟶ Y),
  AlgebraicGeometry.affineLocally (fun {R S} [CommRing R] [CommRing S] => P) f ↔
    ∀ (U : ↑Y.affineOpens) (V : ↑X.affineOpens) (e : ↑V ≤ (TopologicalSpace.Opens.map f.base).obj ↑U),
      P (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appLE f (↑U) (↑V) e))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

5 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound