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AlgebraicGeometry.Scheme.AffineZariskiSite

AlgebraicGeometry.Scheme → Type u

X.AffineZariskiSite is the small affine Zariski site of X, whose elements are affine open sets of X, and whose arrows are basic open sets D(f) ⟶ U for any f : Γ(X, U). Note that this differs from the definition on stacks project where the arrows in the small affine Zariski site are arbitrary inclusions.

Defined in
Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski
Cited by
30 results in Mathlib
Foundations
Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.Scheme.Hom.toNormalization · cited by 28Hom.toNormalizationAlgebraicGeometry.Scheme.AffineZariskiSite.toOpens · cited by 17AffineZariskiSite.toOpensAlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor · cited by 17AffineZariskiSite.toOpens…AlgebraicGeometry.Scheme.AffineZariskiSite.basicOpen · cited by 9AffineZariskiSite.basicOp…AlgebraicGeometry.Scheme.AffineZariskiSite.directedCover · cited by 9AffineZariskiSite.directe…AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections · cited by 5AffineZariskiSite.presiev…AlgebraicGeometry.Scheme.AffineZariskiSite.relativeGluingData · cited by 5AffineZariskiSite.relativ…AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.Scheme.AffineZariskiSite.basicOpen_le · cited by 4AffineZariskiSite.basicOp…AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc · cited by 4Hom.toNormalization_norma…AlgebraicGeometry.Scheme.AffineZariskiSite.sectionsOfPresieve · cited by 3AffineZariskiSite.section…AlgebraicGeometry.Scheme.AffineZariskiSite.grothendieckTopology · cited by 3AffineZariskiSite.grothen…AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_sectionsOfPresieve · cited by 2AffineZariskiSite.presiev…AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec · cited by 2AffineZariskiSite.restric…AlgebraicGeometry.Scheme.Hom.ι_toNormalization · cited by 2Hom.ι_toNormalizationAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.IsAffineOpen · cited by 222AlgebraicGeometry.IsAffin…Scheme.AffineZariskiSiteCITED BYCITES

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