Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_of_res_zero_of_qcqs

∀ {X : AlgebraicGeometry.Scheme} {U : TopologicalSpace.Opens ↥X},
  IsCompact U.carrier →
    IsQuasiSeparated U.carrier →
      ∀ {f s : ↑(X.presheaf.obj (Opposite.op U))},
        TopCat.Presheaf.restrictOpen f (X.basicOpen s) ⋯ = 0 → ∃ n, s ^ n * f = 0

Defined in: Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated
Cited by: 1 results in Mathlib
Foundations: Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites23

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

CategoryTheory.Functor.objstatement and proof · cited by 19,642
RingHomstatement · cited by 10,189
Oppositestatement · cited by 8,081
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
MulZeroClass.mul_zeroproof · cited by 2,091
TopologicalSpace.Opensstatement and proof · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.exists_of_res_zero_of_qcqs_of_topproof · cited by 1