Theorems · Theorem · algebraic geometry
AlgebraicGeometry.finite_irreducibleComponents_of_isNoetherian
∀ {X : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsNoetherian X], (irreducibleComponents ↥X).FiniteA Noetherian scheme has a finite number of irreducible components.
- Defined in
- Mathlib.AlgebraicGeometry.Noetherian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- Set.Finitestatement · cited by 1,814
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- irreducibleComponentsstatement · cited by 35
- AlgebraicGeometry.IsNoetherianstatement and proof · cited by 10
- TopologicalSpace.NoetherianSpace.finite_irreducibleComponentsproof · cited by 3
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