Theorems · Theorem · algebraic geometry
AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompact
∀ {S : AlgebraicGeometry.Scheme} (𝒰 : CategoryTheory.PreZeroHypercover S) [AlgebraicGeometry.QuasiCompactCover 𝒰]
{U : S.Opens},
IsCompact ↑U → ∃ n f V, (∀ (i : Fin n), AlgebraicGeometry.IsAffineOpen (V i)) ∧ ⋃ i, ⇑(𝒰.f (f i)) '' ↑(V i) = ↑U- Cited by
- 1 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.iUnionstatement and proof · cited by 2,483
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensproof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.QuasiCompactCover.exists_homproof · cited by 1