toSpec_bijective — Mathlib

English

The two-way construction yields a bijection between Spec of A⁰_f and Proj|D(f).

Русский

Две конструирования образуют биекцию между Spec A⁰_f и Proj|D(f).

LaTeX

$$$toSpec & fromSpec form a bijection between \mathrm{Spec}(A^0_f) and \mathrm{Proj|D(f)}$$$

Lean4

theorem toSpec_bijective {f : A} {m : ℕ} (f_deg : f ∈ 𝒜 m) (hm : 0 < m) :
    Function.Bijective (toSpec (𝒜 := 𝒜) (f := f)) :=
  ⟨toSpec_injective 𝒜 f_deg hm, toSpec_surjective 𝒜 f_deg hm⟩

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