Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAt

∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {x : ↥X},
  AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt f x →
    ∀ {V : X.Opens} (hV : AlgebraicGeometry.IsAffineOpen V) {U : Y.Opens},
      AlgebraicGeometry.IsAffineOpen U →
        ∀ (hVU : V ≤ (TopologicalSpace.Opens.map f.base).obj U) (hxV : x ∈ V.carrier),
          (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appLE f U V hVU)).QuasiFiniteAt
            (hV.primeIdealOf ⟨x, hxV⟩).asIdeal

Defined in: Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite
Cited by: 1 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

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Cited by1

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AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1