Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Spec
CategoryTheory.Functor CommRingCatᵒᵖ AlgebraicGeometry.Scheme
The spectrum, as a contravariant functor from commutative rings to schemes.
- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.unopproof · cited by 903
- AlgebraicGeometry.Specproof · cited by 626
- AlgebraicGeometry.Spec.mapproof · cited by 332
Cited by80
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.isoSpecproof · cited by 48
- AlgebraicGeometry.pullbackSpecIsoproof · cited by 26
- AlgebraicGeometry.ΓSpec.adjunctionstatement · cited by 16
- AlgebraicGeometry.Spec.preimageproof · cited by 14
- AlgebraicGeometry.algSpecproof · cited by 13
- AlgebraicGeometry.Spec.map_preimageproof · cited by 11
- AlgebraicGeometry.SpecMap_ΓSpecIso_homproof · cited by 8
- AlgebraicGeometry.AffineSpace.SpecIsoproof · cited by 7
- AlgebraicGeometry.pullbackSpecIso_inv_fstproof · cited by 7
- AlgebraicGeometry.pullbackSpecIso_inv_sndproof · cited by 6
- AlgebraicGeometry.Scheme.AffineZariskiSite.relativeGluingDataproof · cited by 5
- AlgebraicGeometry.Scheme.SpecΓIdentitystatement · cited by 5