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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.eq_zero_of_basicOpen_eq_bot

∀ {X : AlgebraicGeometry.Scheme} [hX : AlgebraicGeometry.IsReduced X] {U : X.Opens}
  (s : ↑(X.presheaf.obj (Opposite.op U))), X.basicOpen s = ⊥ → s = 0
Defined in
Mathlib.AlgebraicGeometry.Properties
Cited by
1 results in Mathlib
Foundations
Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsReduced
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AlgebraicGeometry.basicOpen_eq_bot_iff · cited by 1AlgebraicGeometry.basicOp…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objRingHom · cited by 10189RingHomTop.top · cited by 9680Top.topCategoryTheory.Functor.map · cited by 8698Functor.mapSetLike.coe · cited by 8199SetLike.coeOpposite · cited by 8081OppositeCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idBot.bot · cited by 4720Bot.botCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.eq_zero_of_…CITED BYCITES

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