Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.isoSpec
(X : AlgebraicGeometry.Scheme) → [AlgebraicGeometry.IsAffine X] → X ≅ AlgebraicGeometry.Spec (X.presheaf.obj (Opposite.op ⊤))
The canonical isomorphism X ≅ Spec Γ(X) for an affine scheme.
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsAffine
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Top.topstatement · cited by 9,680
- Oppositestatement · cited by 8,081
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by59
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.isoSpecproof · cited by 48
- AlgebraicGeometry.AffineSpace.isoOfIsAffineproof · cited by 10
- AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpecproof · cited by 8
- AlgebraicGeometry.IsAffineOpen.range_fromSpecproof · cited by 8
- AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrankproof · cited by 6
- AlgebraicGeometry.arrowIsoSpecΓOfIsAffineproof · cited by 4
- AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkproof · cited by 3
- AlgebraicGeometry.IsAffineOpen.fromSpec_topstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.isoSpec_Spec_invstatement · cited by 3
- AlgebraicGeometry.isBasis_basicOpenproof · cited by 3
- AlgebraicGeometry.compactSpace_iff_existsproof · cited by 2
- AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_overstatement and proof · cited by 2