English
Let X be integral and U a nonempty open. The map Γ(X,U) → k(X) is injective.
Русский
Пусть X целый, U непустое открытое. Отображение Γ(X,U) → k(X) инъективно.
LaTeX
$$$\forall X\,[\operatorname{IsIntegral} X],\ \forall U\subseteq X,[\operatorname{Nonempty} U],\\; \operatorname{germToFunctionField}(X,U)\text{ is injective}$$$
Lean4
noncomputable instance stalkFunctionFieldAlgebra [IrreducibleSpace X] (x : X) :
Algebra (X.presheaf.stalk x) X.functionField := by
-- TODO: can we write this normally after the refactor finishes?
apply RingHom.toAlgebra
exact (X.presheaf.stalkSpecializes ((genericPoint_spec X).specializes trivial)).hom