AlgebraicGeometry.Scheme.fromSpecStalk

(X : AlgebraicGeometry.Scheme) → (x : ↥X) → AlgebraicGeometry.Spec (X.presheaf.stalk x) ⟶ X

If x is a point of X, this is the canonical morphism from Spec(O_x) to X.

Defined in: Mathlib.AlgebraicGeometry.Stalk
Cited by: 43 results in Mathlib
Foundations: Depth 146 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
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.PresheafedSpace.presheafstatement · cited by 1,104
AlgebraicGeometry.Specstatement · cited by 626
TopCat.Presheaf.stalkstatement · cited by 407
AlgebraicGeometry.IsAffineOpen.fromSpecStalkproof · cited by 5

Results whose statement or proof uses this declaration.