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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpen

∀ {X : AlgebraicGeometry.Scheme} (s : Set ↑(X.presheaf.obj (Opposite.op ⊤))),
  Ideal.span s = ⊤ → (∀ i ∈ s, AlgebraicGeometry.IsAffineOpen (X.basicOpen i)) → AlgebraicGeometry.IsAffine X

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

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Affine
Cited by
2 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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AlgebraicGeometry.affineAnd_isLocal · cited by 2AlgebraicGeometry.affineA…AlgebraicGeometry.isAffineOpen_of_isAffineOpen_basicOpen · cited by 0AlgebraicGeometry.isAffin…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objFinset · cited by 13712FinsetTop.top · cited by 9680Top.topSetLike.coe · cited by 8199SetLike.coeOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.Elem · cited by 7166Set.ElemCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso.inv · cited by 6514Iso.invIdeal · cited by 4748IdealCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homCategoryTheory.Functor.id · cited by 3333Functor.idAlgebraicGeometry.isAffine_of…CITED BYCITES

Cites76

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Cited by2

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