Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_isAffineOpen_preimage_eq

∀ {I : Type u} [inst : CategoryTheory.Category.{u, u} I] (D : CategoryTheory.Functor I AlgebraicGeometry.Scheme)
  (c : CategoryTheory.Limits.Cone D) (hc : CategoryTheory.Limits.IsLimit c) [CategoryTheory.IsCofiltered I]
  [∀ {i j : I} (f : i ⟶ j), AlgebraicGeometry.IsAffineHom (D.map f)] [∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)]
  (U : c.pt.Opens),
  AlgebraicGeometry.IsAffineOpen U →
    ∃ i V, AlgebraicGeometry.IsAffineOpen V ∧ (TopologicalSpace.Opens.map (c.π.app i).base).obj V = U

[Stacks Tag 01Z4](https://stacks.math.columbia.edu/tag/01Z4) ((1))

Defined in

Mathlib.AlgebraicGeometry.AffineTransitionLimit

Cited by

1 results in Mathlib

Foundations

Depth 242 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredAlgebraicGeometry.IsAffineHomQuasiSeparatedSpace