Theorems · Theorem · algebraic geometry

AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated

∀ (X : AlgebraicGeometry.Scheme) (U : X.Opens),
  IsCompact U.carrier →
    IsQuasiSeparated U.carrier →
      ∀ (f : ↑(X.presheaf.obj (Opposite.op U))) (x : ↑(X.presheaf.obj (Opposite.op (X.basicOpen f)))),
        ∃ n y,
          TopCat.Presheaf.restrictOpen y (X.basicOpen f) ⋯ = TopCat.Presheaf.restrictOpen f (X.basicOpen f) ⋯ ^ n * x

Defined in

Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound