AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem

{X : AlgebraicGeometry.Scheme} → (U : X.Opens) → (x : ↥X) → x ∈ U → (AlgebraicGeometry.Spec (X.presheaf.stalk x) ⟶ ↑U)

The canonical map Spec 𝒪_{X, x} ⟶ U given x ∈ U ⊆ X.

Defined in: Mathlib.AlgebraicGeometry.Stalk
Cited by: 8 results in Mathlib
Foundations: Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

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

Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
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
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
AlgebraicGeometry.PresheafedSpace.presheafstatement · cited by 1,104
AlgebraicGeometry.Specstatement · cited by 626

Results whose statement or proof uses this declaration.