Theorems · Definition · algebraic geometry
AlgebraicGeometry.Spec.locallyRingedSpaceObj
CommRingCat → AlgebraicGeometry.LocallyRingedSpace
The spectrum of a commutative ring, as a LocallyRingedSpace.
- Defined in
- Mathlib.AlgebraicGeometry.Spec
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.LocallyRingedSpacestatement · cited by 205
- AlgebraicGeometry.SheafedSpaceproof · cited by 142
- AlgebraicGeometry.Spec.sheafedSpaceObjproof · cited by 24
Cited by72
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Specproof · cited by 626
- AlgebraicGeometry.Spec.toLocallyRingedSpaceproof · cited by 30
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpecstatement · cited by 13
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrierstatement and proof · cited by 9
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpecstatement · cited by 9
- AlgebraicGeometry.Spec.locallyRingedSpaceMapstatement · cited by 7
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdealstatement and proof · cited by 4
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFunstatement and proof · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.toΓSpecstatement · cited by 4
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFunstatement · cited by 3
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eqstatement · cited by 3
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.denom_notMemstatement and proof · cited by 2