Theorems · Theorem · algebraic geometry

AlgebraicGeometry.StructureSheaf.const_ext

∀ {R M : Type u} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {f₁ f₂ : M} {g₁ g₂ : R}
  {U : TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R)} {hu₁ : U ≤ PrimeSpectrum.basicOpen g₁}
  {hu₂ : U ≤ PrimeSpectrum.basicOpen g₂},
  g₂ • f₁ = g₁ • f₂ →
    AlgebraicGeometry.StructureSheaf.const f₁ g₁ U hu₁ = AlgebraicGeometry.StructureSheaf.const f₂ g₂ U hu₂

Defined in

Mathlib.AlgebraicGeometry.StructureSheaf

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule