basicOpenIso — Mathlib

English

Duplicate statement reaffirming surjectivity of toBasicOpen onto basicOpen sections.

Русский

Дублирующее утверждение о сюръективности toBasicOpen на секциях базового открытого.

LaTeX

$$$Function.Surjective (toBasicOpen R f)$$$

Lean4

/-- The ring isomorphism between the structure sheaf on `basicOpen f` and the localization of `R`
at the submonoid of powers of `f`. -/
def basicOpenIso (f : R) :
    (structureSheaf R).1.obj (op (PrimeSpectrum.basicOpen f)) ≅ CommRingCat.of (Localization.Away f) :=
  (asIso (CommRingCat.ofHom (toBasicOpen R f))).symm

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