AlgebraicGeometry.Scheme.irreducibleComponent

(X : AlgebraicGeometry.Scheme) →
  (Z : Set ↥X) → Z ∈ irreducibleComponents ↥X → [AlgebraicGeometry.IsNoetherian X] → AlgebraicGeometry.Scheme

The subscheme structure on an irreducible component of a Noetherian scheme.

Defined in: Mathlib.AlgebraicGeometry.IdealSheaf.IrreducibleComponent
Cited by: 1 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsNoetherian

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

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.IdealSheafData.subschemeproof · cited by 36
irreducibleComponentsstatement and proof · cited by 35
AlgebraicGeometry.IsNoetherianstatement and proof · cited by 10
AlgebraicGeometry.Scheme.irreducibleComponentIdealproof · cited by 2

Results whose statement or proof uses this declaration.