Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.fromSpecStalk_eq_fromSpecStalk
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U) {x : ↥X} (hxU : x ∈ U),
hU.fromSpecStalk hxU = X.fromSpecStalk x- Defined in
- Mathlib.AlgebraicGeometry.Stalk
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.presheafstatement · cited by 1,104
- AlgebraicGeometry.Specstatement · cited by 626
- TopCat.Presheaf.stalkstatement · cited by 407
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
- AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalkproof · cited by 6
- AlgebraicGeometry.Spec.fromSpecStalk_eqproof · cited by 4
- AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkproof · cited by 3
- AlgebraicGeometry.Scheme.fromSpecStalk_appproof · cited by 2
- AlgebraicGeometry.spread_out_of_isGermInjectiveproof · cited by 1