Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_of_res_eq_of_qcqs_of_top

∀ {X : AlgebraicGeometry.Scheme} [CompactSpace ↥X] [QuasiSeparatedSpace ↥X] {f g s : ↑(X.presheaf.obj (Opposite.op ⊤))},
  TopCat.Presheaf.restrictOpen f (X.basicOpen s) ⋯ = TopCat.Presheaf.restrictOpen g (X.basicOpen s) ⋯ →
    ∃ n, s ^ n * f = s ^ n * g

Defined in

Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompactSpaceQuasiSeparatedSpace