Theorems · Theorem · algebraic geometry

AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero

∀ (X : AlgebraicGeometry.LocallyRingedSpace) {U : TopologicalSpace.Opens ↑X.toTopCat}
  (f : ↑(X.presheaf.obj (Opposite.op U))),
  X.toRingedSpace.basicOpen f = ⊥ ↔ ∀ (x : ↥U), (CategoryTheory.ConcreteCategory.hom (X.evaluation x)) f = 0

Defined in: Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField
Cited by: 1 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites22

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
CategoryTheory.Functor.objstatement and proof · cited by 19,642
RingHomstatement · cited by 10,189
Oppositestatement · cited by 8,081
Bot.botstatement and proof · cited by 4,720
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement and proof · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zeroproof · cited by 0