Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.genericPoint_mem_smoothLocus_of_perfectField

∀ {X : AlgebraicGeometry.Scheme} {K : Type u} [inst : Field K] [PerfectField K]
  [inst_2 : AlgebraicGeometry.IsIntegral X] (f : X ⟶ AlgebraicGeometry.Spec (CommRingCat.of K))
  [inst_3 : AlgebraicGeometry.LocallyOfFinitePresentation f],
  genericPoint ↥X ∈ AlgebraicGeometry.Scheme.Hom.smoothLocus f

Defined in: Mathlib.AlgebraicGeometry.Morphisms.Smooth
Cited by: 1 results in Mathlib
Foundations: Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field PerfectField AlgebraicGeometry.IsIntegral AlgebraicGeometry.LocallyOfFinitePresentation

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Cited by1

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AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldproof · cited by 0