Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine
∀ (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsAffine X] (s : Set ↥X), IsClosed s ↔ ∃ I, s = X.zeroLocus ↑I
If X is an affine scheme, every closed set of X is the zero locus
of a set of global sections.
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsAffine
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Cites43
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- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
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