Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Proj.val_sectionInBasicOpen_apply
∀ {A σ : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] {𝒜 : ℕ → σ}
[inst_3 : GradedRing 𝒜] (p : ↑(ProjectiveSpectrum.top 𝒜))
(c : HomogeneousLocalization.NumDenSameDeg 𝒜 p.asHomogeneousIdeal.toIdeal.primeCompl)
(q : ↥(ProjectiveSpectrum.basicOpen 𝒜 ↑c.den)),
HomogeneousLocalization.val (↑(AlgebraicGeometry.sectionInBasicOpen 𝒜 p c) q) = Localization.mk ↑c.num ⟨↑c.den, ⋯⟩- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- TopCat.carrierstatement and proof · cited by 3,184
- Submonoidstatement · cited by 3,086
- Opposite.unopstatement · cited by 2,231
- TopologicalSpace.Opensstatement · cited by 2,040
- SetLikestatement and proof · cited by 1,084
- Ideal.primeComplstatement and proof · cited by 462
- GradedRingstatement and proof · cited by 424
- Localizationstatement · cited by 270
- AddSubgroupClassstatement and proof · cited by 240
- Localization.mkstatement · cited by 110
- HomogeneousIdeal.toIdealstatement and proof · cited by 105
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