English
The inverse of the ΓIsoTop is given by the inverse of the app map on the open ranges.
Русский
Обратный изоморфизм ΓIsoTop задаётся как обратная к карте на открытых диапазонах.
LaTeX
$$$ (\ΓIsoTop f U)^{-1} = \text{inv map on opensRange } f $$$
Lean4
/-- If `f` is an open immersion `X ⟶ Y`, the global sections of `X`
are naturally isomorphic to the sections of `Y` over the image of `f`. -/
noncomputable def ΓIso {X Y : Scheme.{u}} (f : X ⟶ Y) [IsOpenImmersion f] (U : Y.Opens) :
Γ(X, f ⁻¹ᵁ U) ≅ Γ(Y, f.opensRange ⊓ U) :=
(f.appIso (f ⁻¹ᵁ U)).symm ≪≫ Y.presheaf.mapIso (eqToIso <| (f.image_preimage_eq_opensRange_inter U).symm).op