Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isSchemeTheoreticallyDominant_iff_isDominant

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f] [AlgebraicGeometry.IsReduced Y],
  AlgebraicGeometry.IsSchemeTheoreticallyDominant f ↔ AlgebraicGeometry.IsDominant f

If the target is reduced and the map is quasi-compact, then scheme-theoretically dominant is equivalent to dominant.

Defined in

Mathlib.AlgebraicGeometry.Morphisms.SchemeTheoreticallyDominant

Cited by

1 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.QuasiCompactAlgebraicGeometry.IsReduced