Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Spec_zeroLocus

∀ {R : CommRingCat} (s : Set ↑((AlgebraicGeometry.Spec R).presheaf.obj (Opposite.op ⊤))),
  (AlgebraicGeometry.Spec R).zeroLocus s =
    PrimeSpectrum.zeroLocus (⇑(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.ΓSpecIso R).inv) ⁻¹' s)

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 1 results in Mathlib
Foundations: Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
CategoryTheory.Functor.objstatement and proof · cited by 19,642
RingHomstatement · cited by 10,189
Top.topstatement and proof · cited by 9,680
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invstatement and proof · cited by 6,514
Set.preimagestatement and proof · cited by 4,946
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement · cited by 3,184
CommRingCatstatement and proof · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6