Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.isLocal_ringHomProperty_of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget

∀ (P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsZariskiLocalAtTarget P]
  [AlgebraicGeometry.IsZariskiLocalAtSource P],
  RingHom.PropertyIsLocal fun {R S} [CommRing R] [CommRing S] f => P (AlgebraicGeometry.Spec.map (CommRingCat.ofHom f))

Defined in: Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
Cited by: 1 results in Mathlib
Foundations: Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsZariskiLocalAtTarget AlgebraicGeometry.IsZariskiLocalAtSource

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Cites45

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Quiver.Homproof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CommRingstatement and proof · cited by 17,173
Algebraproof · cited by 11,388
RingHomstatement and proof · cited by 10,189
Top.topproof · cited by 9,680
Set.Elemproof · cited by 7,166
Algebra.algebraMapproof · cited by 4,706
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179

Cited by1

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AlgebraicGeometry.HasRingHomProperty.of_isZariskiLocalAtSource_of_isZariskiLocalAtTargetproof · cited by 2