Theorems · Theorem · algebraic geometry
ProjectiveSpectrum.zeroLocus_sup_ideal
∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubmonoidClass σ A] (𝒜 : ℕ → σ)
[inst_3 : GradedRing 𝒜] (I J : Ideal A),
ProjectiveSpectrum.zeroLocus 𝒜 ↑(I ⊔ J) = ProjectiveSpectrum.zeroLocus 𝒜 ↑I ∩ ProjectiveSpectrum.zeroLocus 𝒜 ↑J- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coestatement · cited by 8,199
- Idealstatement and proof · cited by 4,748
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- ProjectiveSpectrumstatement · cited by 86
- GaloisConnection.l_supproof · cited by 81
- ProjectiveSpectrum.zeroLocusstatement · cited by 42
- ProjectiveSpectrum.gc_idealproof · cited by 12
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