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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.GeometricallyIntegral.isIntegral_of_isLocallyNoetherian

∀ {X S : AlgebraicGeometry.Scheme} (f : X ⟶ S) [AlgebraicGeometry.GeometricallyIntegral f] [AlgebraicGeometry.Flat f]
  [AlgebraicGeometry.UniversallyOpen f] [AlgebraicGeometry.IsIntegral S] [AlgebraicGeometry.IsLocallyNoetherian S],
  AlgebraicGeometry.IsIntegral X
Defined in
Mathlib.AlgebraicGeometry.Geometrically.Integral
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Foundations
Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.GeometricallyIntegralAlgebraicGeometry.FlatAlgebraicGeometry.UniversallyOpenAlgebraicGeometry.IsIntegralAlgebraicGeometry.IsLocallyNoetherian
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Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Flat · cited by 49AlgebraicGeometry.FlatAlgebraicGeometry.IsIntegral · cited by 45AlgebraicGeometry.IsInteg…AlgebraicGeometry.IsLocallyNoetherian · cited by 31AlgebraicGeometry.IsLocal…AlgebraicGeometry.GeometricallyIntegral · cited by 9AlgebraicGeometry.Geometr…AlgebraicGeometry.UniversallyOpen · cited by 8AlgebraicGeometry.Univers…AlgebraicGeometry.Scheme.Hom.isOpenMap · cited by 5Hom.isOpenMapAlgebraicGeometry.GeometricallyIrreducible.irreducibleSpace · cited by 2GeometricallyIrreducible.…AlgebraicGeometry.GeometricallyReduced.isReduced_of_flat_of_isLocallyNoetherian · cited by 2GeometricallyReduced.isRe…AlgebraicGeometry.isIntegral_iff_irreducibleSpace_and_isReduced · cited by 2AlgebraicGeometry.isInteg…GeometricallyIntegral.isInteg…CITED BYCITES

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