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chore(AlgebraicGeometry): change definition of Zariski topology (#28603)
This PR changes the definition of the Zariski topology on `Scheme` from `zariskiPretopology.toGrothendieck` to `grothendieckTopology IsOpenImmersion`. Note that `grothendieckTopology` is an `abbrev` that uses `toGrothendieck`, so this definition should be strictly better and strictly unfolds to the old definition.
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Mathlib/AlgebraicGeometry/Sites/BigZariski.lean

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@@ -35,12 +35,14 @@ namespace AlgebraicGeometry
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namespace Scheme
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/-- The Zariski pretopology on the category of schemes. -/
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def zariskiPretopology : Pretopology (Scheme.{u}) :=
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def zariskiPretopology : Pretopology Scheme.{u} :=
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pretopology @IsOpenImmersion
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/-- The Zariski topology on the category of schemes. -/
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abbrev zariskiTopology : GrothendieckTopology (Scheme.{u}) :=
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zariskiPretopology.toGrothendieck
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abbrev zariskiTopology : GrothendieckTopology Scheme.{u} :=
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grothendieckTopology IsOpenImmersion
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lemma zariskiTopology_eq : zariskiTopology.{u} = zariskiPretopology.toGrothendieck := rfl
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instance subcanonical_zariskiTopology : zariskiTopology.Subcanonical := by
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apply GrothendieckTopology.Subcanonical.of_isSheaf_yoneda_obj

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