restrict — Mathlib

English

If R is a ring and f ∈ R, the localization away f yields an open immersion Spec.map (algebraMap R (Localization.Away f)).

Русский

Локализация away f даёт открытое вложение Spec.map (algebraMap ...).

LaTeX

$$$$ \text{IsOpenImmersion}(\operatorname{Spec}(\text{Localization Away}(f))) $$$$

Lean4

/-- The restriction of a Scheme along an open embedding. -/
@[simps! -isSimp carrier, simps! presheaf_obj]
def restrict : Scheme :=
  { PresheafedSpace.IsOpenImmersion.toScheme X (X.toPresheafedSpace.ofRestrict h) with
    toPresheafedSpace := X.toPresheafedSpace.restrict h }

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