Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.irreducibleComponentIdeal
(X : AlgebraicGeometry.Scheme) → (Z : Set ↥X) → Z ∈ irreducibleComponents ↥X → [AlgebraicGeometry.IsNoetherian X] → X.IdealSheafData
The ideal sheaf data associated to an irreducible component of a Noetherian scheme.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 179 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.
- Setstatement and proof · cited by 53,352
- 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.Opens.ιproof · cited by 275
- AlgebraicGeometry.Scheme.IdealSheafDatastatement and proof · cited by 192
- AlgebraicGeometry.Scheme.IdealSheafData.idealproof · cited by 88
- AlgebraicGeometry.Scheme.Hom.kerproof · cited by 51
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.irreducibleComponentιproof · cited by 1
- AlgebraicGeometry.Scheme.irreducibleComponentproof · cited by 1
- AlgebraicGeometry.Scheme.irreducibleComponentIdeal_defstatement · cited by 0
- AlgebraicGeometry.Scheme.irreducibleComponentι_applystatement · cited by 0