Theorems · Theorem · algebraic geometry
ProjectiveSpectrum.zeroLocus_empty_of_one_mem
∀ {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] {s : Set A}, 1 ∈ s → ProjectiveSpectrum.zeroLocus 𝒜 s = ∅- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CommRingstatement and proof · cited by 17,173
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- HomogeneousIdeal.toIdealproof · cited by 105
- ProjectiveSpectrumstatement and proof · cited by 86
- Ideal.IsPrime.ne_topproof · cited by 82
- ProjectiveSpectrum.asHomogeneousIdealproof · cited by 61
- Ideal.eq_top_iff_oneproof · cited by 56
- ProjectiveSpectrum.zeroLocusstatement and proof · cited by 42
- Set.eq_empty_iff_forall_notMemproof · cited by 42
Cited by2
Results whose statement or proof uses this declaration.
- ProjectiveSpectrum.zeroLocus_singleton_oneproof · cited by 1
- ProjectiveSpectrum.zeroLocus_univproof · cited by 0